Battery pack capacity estimation under real-world operating conditions is important for battery performance optimization and health management,contributing to the reliability and longevity of batterypowered systems.Ho...Battery pack capacity estimation under real-world operating conditions is important for battery performance optimization and health management,contributing to the reliability and longevity of batterypowered systems.However,complex operating conditions,coupling cell-to-cell inconsistency,and limited labeled data pose great challenges to accurate and robust battery pack capacity estimation.To address these issues,this paper proposes a hierarchical data-driven framework aimed at enhancing the training of machine learning models with fewer labeled data.Unlike traditional data-driven methods that lack interpretability,the hierarchical data-driven framework unveils the“mechanism”of the black box inside the data-driven framework by splitting the final estimation target into cell-level and pack-level intermediate targets.A generalized feature matrix is devised without requiring all cell voltages,significantly reducing the computational cost and memory resources.The generated intermediate target labels and the corresponding features are hierarchically employed to enhance the training of two machine learning models,effectively alleviating the difficulty of learning the relationship from all features due to fewer labeled data and addressing the dilemma of requiring extensive labeled data for accurate estimation.Using only 10%of degradation data,the proposed framework outperforms the state-of-the-art battery pack capacity estimation methods,achieving mean absolute percentage errors of 0.608%,0.601%,and 1.128%for three battery packs whose degradation load profiles represent real-world operating conditions.Its high accuracy,adaptability,and robustness indicate the potential in different application scenarios,which is promising for reducing laborious and expensive aging experiments at the pack level and facilitating the development of battery technology.展开更多
Commutators of Calderon-Zygmund operators on product spaces to be study in the paper is the commutators of Sarah H Ferguson and Michael T Lacey. The L^P boundedness of the nested commutators is proved on product space...Commutators of Calderon-Zygmund operators on product spaces to be study in the paper is the commutators of Sarah H Ferguson and Michael T Lacey. The L^P boundedness of the nested commutators is proved on product spaces, where 1<p<∞.展开更多
We demonstrate a stable Q-switched mode-locked erbium-doped fiber laser (EDFL) operating in dark regime based on the nonlinear polarization rotation technique. The EDFL produces a pulse train where the Q-switching e...We demonstrate a stable Q-switched mode-locked erbium-doped fiber laser (EDFL) operating in dark regime based on the nonlinear polarization rotation technique. The EDFL produces a pulse train where the Q-switching envelope is formed by multiple dark pulses. The repetition rate of the Q-switched envelope can be increased from 0.96kHz to 3.26kHz, whereas the pulse width reduces from 211 #s to 86#s. The highest pulse of 479nJ is obtained at the pump power of 55 mW. It is also observed that the dark pulses inside the Q-switching envelope consist of two parts: square and trailing dark pulses. The shortest pulse width of the dark square pulse is obtained at 40.5μs when the pump power is fixed at 145mW. The repetition rate of trailing dark pulses can be increased from 27.62kHz to 50kHz as the pump power increases from 55mW to 145mW.展开更多
The paper introduces the present status and development objec- tives of the operational support systems of the three telecommuni- cation operators in China and briefly describes the features of the new generation tele...The paper introduces the present status and development objec- tives of the operational support systems of the three telecommuni- cation operators in China and briefly describes the features of the new generation telecommunication operational support system (NGOSS),such as adopting the TMN/TOM structure,supporting the unified and multiple access processing,conducting effective and centralized management of data.展开更多
Currently, the production and the number of installations of PV (photovoltaic) modules have been increasing rapidly because of a feed-in tariff in Japan. Accordingly, the number of failures has also increased. Many ...Currently, the production and the number of installations of PV (photovoltaic) modules have been increasing rapidly because of a feed-in tariff in Japan. Accordingly, the number of failures has also increased. Many failures are a result of the Hot-Spot phenomenon in which defective cell becomes hot when shadow occurs on the cell, On the other hand, if shadow occurs on normal cell, there are cases that P&O method that is MPPT (maximum power point tracking) control method incorporated in conventional PV system cannot track maximum power point and generated power decreases. The correspondence is required rapidly if these trouble occur. However, conventional PV system monitors generated power, correspondence is impossible by monitoring generated power. Previously, the authors developed real time Hot-Spot detection system that incorporates into PCS (power conditioning system). Thus, the authors developed plug-in type Hot-Spot monitoring system that includes "PV peak shift method" and confirmed effectiveness of the system in this time. "PV peak shift method" loads "Scan method" that is MPPT control method and measures I-V (current-voltage) characteristic by changing voltage of module from open to short by "Scan method" on a regular basis. The developed Hot-Spot monitoring system uses slope of I-V characteristic of PV module. Inserting developed system into already installed PV system, Hot-Spot can be easily monitored in real time and PV system can be operated at maximum power point.展开更多
In this article, we consider a fast algorithm for first generation Calderon-Zygmund operators. First, we estimate the convergence speed of the relative approximation algorithm. Then, we establish the continuity on Bes...In this article, we consider a fast algorithm for first generation Calderon-Zygmund operators. First, we estimate the convergence speed of the relative approximation algorithm. Then, we establish the continuity on Besov spaces and Triebel-Lizorkin spaces for the oper- ators with rough kernel.展开更多
In this paper, we discuss the multilinear commutator of Θ-type Calder6n- Zygmund operators, and obtain that this kind of multilinear commutators is bounded from LP(Rn) to Lq(Rn), from LP(Rn) to Triebel-Lizorkin...In this paper, we discuss the multilinear commutator of Θ-type Calder6n- Zygmund operators, and obtain that this kind of multilinear commutators is bounded from LP(Rn) to Lq(Rn), from LP(Rn) to Triebel-Lizorkin spaces and on certain Hardy type spaces.展开更多
Sphere packing is an attractive way to generate high quality mesh. Several algorithms have been proposed in this topic, however these algorithms are not sufficiently fast for large scale problems. The paper presents a...Sphere packing is an attractive way to generate high quality mesh. Several algorithms have been proposed in this topic, however these algorithms are not sufficiently fast for large scale problems. The paper presents an efficient sphere packing algorithm which is much faster and appears to be the most practical among all sphere packing methods presented so far for mesh generation. The algorithm packs spheres inside a domain using advancing front method. High efficiency has resulted from a concept of 4R measure, which localizes all the computations involved in the whole sphere packing process.展开更多
In this article, the author introduces a class of non-convolution Calder′on-Zygmund operators whose kernels are certain sums involving the products of Meyer wavelets and their convolutions. The boundedness on Besov s...In this article, the author introduces a class of non-convolution Calder′on-Zygmund operators whose kernels are certain sums involving the products of Meyer wavelets and their convolutions. The boundedness on Besov spaces Bp^0 ,q(1 ≤p,q ≤∞) is also obtained. Moreover, as an application, the author gives a brief proof of the known result that Hrmander condition can ensure the boundedness of convolution-type Calder′on-Zygmund operators on Besov spaces B^p0 ,q(1 ≤p,q ≤∞). However, the proof is quite different from the previous one.展开更多
In this note, the authors prove that the commutator Tb, generated by θ-type Calderon-Zygmund operator T and a Lipschitz function b is bounded from LP(R^n) intoLip(β_n/p)(R^n) and also maps from Ln/β (R^n) i...In this note, the authors prove that the commutator Tb, generated by θ-type Calderon-Zygmund operator T and a Lipschitz function b is bounded from LP(R^n) intoLip(β_n/p)(R^n) and also maps from Ln/β (R^n) into BMO(R^n).展开更多
Let 0 〈 p ≤ 1 and w in the Muckenhoupt class A1. Recently, by using the weighted atomic decomposition and molecular characterization, Lee, Lin and yang[11] established that the Riesz transforms R j, j = 1,2,..., n, ...Let 0 〈 p ≤ 1 and w in the Muckenhoupt class A1. Recently, by using the weighted atomic decomposition and molecular characterization, Lee, Lin and yang[11] established that the Riesz transforms R j, j = 1,2,..., n, are bounded on Hwp (Rn). In this note we extend this to the general case of weight w in the Muckenhoupt class A.. through molecular characterization. One difficulty, which has not been taken care in [11] consists in passing from atoms to all functions in HwP(Rn). Furthermore, the HwP-boundedness of θ- Calderon-Zygmund operators are also given through molecular characterization and atomic decomposition.展开更多
The main focus of this study is to investigate the impact of heat generation/absorption with ramp velocity and ramp temperature on magnetohydrodynamic(MHD)time-dependent Maxwell fluid over an unbounded plate embedded ...The main focus of this study is to investigate the impact of heat generation/absorption with ramp velocity and ramp temperature on magnetohydrodynamic(MHD)time-dependent Maxwell fluid over an unbounded plate embedded in a permeable medium.Non-dimensional parameters along with Laplace transformation and inversion algorithms are used to find the solution of shear stress,energy,and velocity profile.Recently,new fractional differential operators are used to define ramped temperature and ramped velocity.The obtained analytical solutions are plotted for different values of emerging parameters.Fractional time derivatives are used to analyze the impact of fractional parameters(memory effect)on the dynamics of the fluid.While making a comparison,it is observed that the fractional-order model is best to explain the memory effect as compared to classical models.Our results suggest that the velocity profile decrease by increasing the effective Prandtl number.The existence of an effective Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity.The incremental value of the M is observed for a decrease in the velocity field,which reflects to control resistive force.Further,it is noted that the Atangana-Baleanu derivative in Caputo sense(ABC)is the best to highlight the dynamics of the fluid.The influence of pertinent parameters is analyzed graphically for velocity and energy profile.Expressions for skin friction and Nusselt number are also derived for fractional differential operators.展开更多
To preserve the sharp features and details of the synthetic aperture radar (SAR) image effectively when despeckling, a despeckling algorithm with edge detection in nonsubsampled second generation bandelet transform ...To preserve the sharp features and details of the synthetic aperture radar (SAR) image effectively when despeckling, a despeckling algorithm with edge detection in nonsubsampled second generation bandelet transform (NSBT) domain is proposed. First, the Canny operator is utilized to detect and remove edges from the SAR image. Then the NSBT which has an optimal approximation to the edges of images and a hard thresholding rule are used to approximate the details while despeckling the edge-removed image. Finally, the removed edges are added to the reconstructed image. As the edges axe detected and protected, and the NSBT is used, the proposed algorithm reaches the state-of-the-art effect which realizes both despeckling and preserving edges and details simultaneously. Experimental results show that both the subjective visual effect and the mainly objective performance indexes of the proposed algorithm outperform that of both Bayesian wavelet shrinkage with edge detection and Bayesian least square-Gaussian scale mixture (BLS-GSM).展开更多
Let be a bounded smooth domain. In this paper, the authors define the Besov spaces Bpap on , establish the atomic decomposition of these spaces, and obtain the regularity estimate of the Dirichlet problem and the Neum...Let be a bounded smooth domain. In this paper, the authors define the Besov spaces Bpap on , establish the atomic decomposition of these spaces, and obtain the regularity estimate of the Dirichlet problem and the Neumann problem for the Laplace operator on these spaces.展开更多
In this paper, some weighted estimates with general weights are established for the m-linear Calderon-Zygmund operator and the corresponding maximal operator. It is proved that, ifp1,…,pm ∈ [1, ∞] and p ∈ (0, ∞...In this paper, some weighted estimates with general weights are established for the m-linear Calderon-Zygmund operator and the corresponding maximal operator. It is proved that, ifp1,…,pm ∈ [1, ∞] and p ∈ (0, ∞) with 1/p = ∑k=1^m 1/pk, then for any weight w, integer l with 1 〈 e 〈 m,展开更多
This paper applies the perspective of business ecosystem to mobile communications industry,trying to help mobile network operators improve their strategies in the era of the third generation mobile communications(3G)....This paper applies the perspective of business ecosystem to mobile communications industry,trying to help mobile network operators improve their strategies in the era of the third generation mobile communications(3G).According to the definition of the business ecosystem,the ecosystem structure of mobile network operators is analyzed.As an important hub in the ecosystem,mobile network operators are advised to take a keystone strategy.The key points of the strategy are summarized.Finally,suggestions for Chinese mobile network operators are given based on the analysis.展开更多
The maximum power point of PV (photovoltaic) generation moves depending on weather conditions and load. Therefore, it is significant to make sure that the panels can work at the maximum power point under MPPT (maxi...The maximum power point of PV (photovoltaic) generation moves depending on weather conditions and load. Therefore, it is significant to make sure that the panels can work at the maximum power point under MPPT (maximum power point tracking) control. However, it has the problems of low efficiency and unstable operation when panels are covered by the partial shadow. The result is that the output power may be substantially decreased. To overcome this issue, the authors propose a new plug-in operation point correction system. This system is put between PV panels and PCS (power conditioning system) in the existing PV generation system. In this paper, the experimental results describe that the output electric energy increases approximately 1.4 times as compared with the conventional system when the proposed correction system is inserted.展开更多
In this paper, the author establishes the boundedness of multilinear operators on weighted Herz spaces and Herz-type Hardy spaces. The author also obtains their weak estimates on endpoints. As a special case, the conc...In this paper, the author establishes the boundedness of multilinear operators on weighted Herz spaces and Herz-type Hardy spaces. The author also obtains their weak estimates on endpoints. As a special case, the conclusions may lead to the weighted estimates for multilinear Calderon-Zygmund operators.展开更多
In this paper, the boundedness in Lebesgue spaces of commutators and multilinear commutators generated by θ-type Calderon-Zygmund operators with RBMO(μ) functions on non-homogeneous metric measure spaces is obtained.
基金supported by the National Outstanding Youth Science Fund Project of National Natural Science Foundation of China[Grant No.52222708]the Natural Science Foundation of Beijing Municipality[Grant No.3212033]。
文摘Battery pack capacity estimation under real-world operating conditions is important for battery performance optimization and health management,contributing to the reliability and longevity of batterypowered systems.However,complex operating conditions,coupling cell-to-cell inconsistency,and limited labeled data pose great challenges to accurate and robust battery pack capacity estimation.To address these issues,this paper proposes a hierarchical data-driven framework aimed at enhancing the training of machine learning models with fewer labeled data.Unlike traditional data-driven methods that lack interpretability,the hierarchical data-driven framework unveils the“mechanism”of the black box inside the data-driven framework by splitting the final estimation target into cell-level and pack-level intermediate targets.A generalized feature matrix is devised without requiring all cell voltages,significantly reducing the computational cost and memory resources.The generated intermediate target labels and the corresponding features are hierarchically employed to enhance the training of two machine learning models,effectively alleviating the difficulty of learning the relationship from all features due to fewer labeled data and addressing the dilemma of requiring extensive labeled data for accurate estimation.Using only 10%of degradation data,the proposed framework outperforms the state-of-the-art battery pack capacity estimation methods,achieving mean absolute percentage errors of 0.608%,0.601%,and 1.128%for three battery packs whose degradation load profiles represent real-world operating conditions.Its high accuracy,adaptability,and robustness indicate the potential in different application scenarios,which is promising for reducing laborious and expensive aging experiments at the pack level and facilitating the development of battery technology.
基金Supported by the National Natural Science Foundation of China(10571182)
文摘Commutators of Calderon-Zygmund operators on product spaces to be study in the paper is the commutators of Sarah H Ferguson and Michael T Lacey. The L^P boundedness of the nested commutators is proved on product spaces, where 1<p<∞.
基金Supported by the Fund from University of Malaya under Grant No RU007/2015LRGS(2015)/NGOD/UM/KPTMOSTI under Grant No SF014-2014
文摘We demonstrate a stable Q-switched mode-locked erbium-doped fiber laser (EDFL) operating in dark regime based on the nonlinear polarization rotation technique. The EDFL produces a pulse train where the Q-switching envelope is formed by multiple dark pulses. The repetition rate of the Q-switched envelope can be increased from 0.96kHz to 3.26kHz, whereas the pulse width reduces from 211 #s to 86#s. The highest pulse of 479nJ is obtained at the pump power of 55 mW. It is also observed that the dark pulses inside the Q-switching envelope consist of two parts: square and trailing dark pulses. The shortest pulse width of the dark square pulse is obtained at 40.5μs when the pump power is fixed at 145mW. The repetition rate of trailing dark pulses can be increased from 27.62kHz to 50kHz as the pump power increases from 55mW to 145mW.
文摘The paper introduces the present status and development objec- tives of the operational support systems of the three telecommuni- cation operators in China and briefly describes the features of the new generation telecommunication operational support system (NGOSS),such as adopting the TMN/TOM structure,supporting the unified and multiple access processing,conducting effective and centralized management of data.
文摘Currently, the production and the number of installations of PV (photovoltaic) modules have been increasing rapidly because of a feed-in tariff in Japan. Accordingly, the number of failures has also increased. Many failures are a result of the Hot-Spot phenomenon in which defective cell becomes hot when shadow occurs on the cell, On the other hand, if shadow occurs on normal cell, there are cases that P&O method that is MPPT (maximum power point tracking) control method incorporated in conventional PV system cannot track maximum power point and generated power decreases. The correspondence is required rapidly if these trouble occur. However, conventional PV system monitors generated power, correspondence is impossible by monitoring generated power. Previously, the authors developed real time Hot-Spot detection system that incorporates into PCS (power conditioning system). Thus, the authors developed plug-in type Hot-Spot monitoring system that includes "PV peak shift method" and confirmed effectiveness of the system in this time. "PV peak shift method" loads "Scan method" that is MPPT control method and measures I-V (current-voltage) characteristic by changing voltage of module from open to short by "Scan method" on a regular basis. The developed Hot-Spot monitoring system uses slope of I-V characteristic of PV module. Inserting developed system into already installed PV system, Hot-Spot can be easily monitored in real time and PV system can be operated at maximum power point.
基金Supported by NNSF of China(11271209,1137105,11571261)and SRFDP(20130003110003)
文摘In this article, we consider a fast algorithm for first generation Calderon-Zygmund operators. First, we estimate the convergence speed of the relative approximation algorithm. Then, we establish the continuity on Besov spaces and Triebel-Lizorkin spaces for the oper- ators with rough kernel.
基金NSF of Anhui Province (No.07021019)Education Committee of Anhui Province (No.KJ2007A009)NSF of Chaohu College(No. XLY-200823)
文摘In this paper, we discuss the multilinear commutator of Θ-type Calder6n- Zygmund operators, and obtain that this kind of multilinear commutators is bounded from LP(Rn) to Lq(Rn), from LP(Rn) to Triebel-Lizorkin spaces and on certain Hardy type spaces.
基金the National Natural Science Foundation of China (10602002 and 10772005)
文摘Sphere packing is an attractive way to generate high quality mesh. Several algorithms have been proposed in this topic, however these algorithms are not sufficiently fast for large scale problems. The paper presents an efficient sphere packing algorithm which is much faster and appears to be the most practical among all sphere packing methods presented so far for mesh generation. The algorithm packs spheres inside a domain using advancing front method. High efficiency has resulted from a concept of 4R measure, which localizes all the computations involved in the whole sphere packing process.
基金Sponsored by the NSF of South-Central University for Nationalities(YZZ08004)NNSF of China (10871209)
文摘In this article, the author introduces a class of non-convolution Calder′on-Zygmund operators whose kernels are certain sums involving the products of Meyer wavelets and their convolutions. The boundedness on Besov spaces Bp^0 ,q(1 ≤p,q ≤∞) is also obtained. Moreover, as an application, the author gives a brief proof of the known result that Hrmander condition can ensure the boundedness of convolution-type Calder′on-Zygmund operators on Besov spaces B^p0 ,q(1 ≤p,q ≤∞). However, the proof is quite different from the previous one.
基金Supported by NSFC(10571014)NSFC(10571156)+1 种基金the Doctor Foundation of Jxnu (2443)the Natural Science Foundation of Jiangxi province(2008GZS0051)
文摘In this note, the authors prove that the commutator Tb, generated by θ-type Calderon-Zygmund operator T and a Lipschitz function b is bounded from LP(R^n) intoLip(β_n/p)(R^n) and also maps from Ln/β (R^n) into BMO(R^n).
文摘Let 0 〈 p ≤ 1 and w in the Muckenhoupt class A1. Recently, by using the weighted atomic decomposition and molecular characterization, Lee, Lin and yang[11] established that the Riesz transforms R j, j = 1,2,..., n, are bounded on Hwp (Rn). In this note we extend this to the general case of weight w in the Muckenhoupt class A.. through molecular characterization. One difficulty, which has not been taken care in [11] consists in passing from atoms to all functions in HwP(Rn). Furthermore, the HwP-boundedness of θ- Calderon-Zygmund operators are also given through molecular characterization and atomic decomposition.
文摘The main focus of this study is to investigate the impact of heat generation/absorption with ramp velocity and ramp temperature on magnetohydrodynamic(MHD)time-dependent Maxwell fluid over an unbounded plate embedded in a permeable medium.Non-dimensional parameters along with Laplace transformation and inversion algorithms are used to find the solution of shear stress,energy,and velocity profile.Recently,new fractional differential operators are used to define ramped temperature and ramped velocity.The obtained analytical solutions are plotted for different values of emerging parameters.Fractional time derivatives are used to analyze the impact of fractional parameters(memory effect)on the dynamics of the fluid.While making a comparison,it is observed that the fractional-order model is best to explain the memory effect as compared to classical models.Our results suggest that the velocity profile decrease by increasing the effective Prandtl number.The existence of an effective Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity.The incremental value of the M is observed for a decrease in the velocity field,which reflects to control resistive force.Further,it is noted that the Atangana-Baleanu derivative in Caputo sense(ABC)is the best to highlight the dynamics of the fluid.The influence of pertinent parameters is analyzed graphically for velocity and energy profile.Expressions for skin friction and Nusselt number are also derived for fractional differential operators.
基金supported by the National Natural Science Foundation of China(6067309760702062)+3 种基金the National HighTechnology Research and Development Program of China(863 Program)(2008AA01Z1252007AA12Z136)the National ResearchFoundation for the Doctoral Program of Higher Education of China(20060701007)the Program for Cheung Kong Scholarsand Innovative Research Team in University(IRT 0645).
文摘To preserve the sharp features and details of the synthetic aperture radar (SAR) image effectively when despeckling, a despeckling algorithm with edge detection in nonsubsampled second generation bandelet transform (NSBT) domain is proposed. First, the Canny operator is utilized to detect and remove edges from the SAR image. Then the NSBT which has an optimal approximation to the edges of images and a hard thresholding rule are used to approximate the details while despeckling the edge-removed image. Finally, the removed edges are added to the reconstructed image. As the edges axe detected and protected, and the NSBT is used, the proposed algorithm reaches the state-of-the-art effect which realizes both despeckling and preserving edges and details simultaneously. Experimental results show that both the subjective visual effect and the mainly objective performance indexes of the proposed algorithm outperform that of both Bayesian wavelet shrinkage with edge detection and Bayesian least square-Gaussian scale mixture (BLS-GSM).
文摘Let be a bounded smooth domain. In this paper, the authors define the Besov spaces Bpap on , establish the atomic decomposition of these spaces, and obtain the regularity estimate of the Dirichlet problem and the Neumann problem for the Laplace operator on these spaces.
文摘In this paper, some weighted estimates with general weights are established for the m-linear Calderon-Zygmund operator and the corresponding maximal operator. It is proved that, ifp1,…,pm ∈ [1, ∞] and p ∈ (0, ∞) with 1/p = ∑k=1^m 1/pk, then for any weight w, integer l with 1 〈 e 〈 m,
文摘This paper applies the perspective of business ecosystem to mobile communications industry,trying to help mobile network operators improve their strategies in the era of the third generation mobile communications(3G).According to the definition of the business ecosystem,the ecosystem structure of mobile network operators is analyzed.As an important hub in the ecosystem,mobile network operators are advised to take a keystone strategy.The key points of the strategy are summarized.Finally,suggestions for Chinese mobile network operators are given based on the analysis.
文摘The maximum power point of PV (photovoltaic) generation moves depending on weather conditions and load. Therefore, it is significant to make sure that the panels can work at the maximum power point under MPPT (maximum power point tracking) control. However, it has the problems of low efficiency and unstable operation when panels are covered by the partial shadow. The result is that the output power may be substantially decreased. To overcome this issue, the authors propose a new plug-in operation point correction system. This system is put between PV panels and PCS (power conditioning system) in the existing PV generation system. In this paper, the experimental results describe that the output electric energy increases approximately 1.4 times as compared with the conventional system when the proposed correction system is inserted.
基金Supported by the National 973 Project and the SEDF of China.
文摘In this paper, the author establishes the boundedness of multilinear operators on weighted Herz spaces and Herz-type Hardy spaces. The author also obtains their weak estimates on endpoints. As a special case, the conclusions may lead to the weighted estimates for multilinear Calderon-Zygmund operators.
基金supported by NSF of Anhui Province(No.1608085QA12)NSF of Education Committee of Anhui Province(Nos.KJ2016A506 and KJ2017A454)+2 种基金Excellent Young Talents Foundation of Anhui Province(No.GXYQ2017070)Doctoral Scientific Research Foundation of Chaohu University(No.KYQD-201605)Scientific Research Project of Chaohu University(No.XLY-201501)
文摘In this paper, the boundedness in Lebesgue spaces of commutators and multilinear commutators generated by θ-type Calderon-Zygmund operators with RBMO(μ) functions on non-homogeneous metric measure spaces is obtained.