For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f...For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.展开更多
We study Hausdorff operators on the product Besov space B0,1 1 (Rn ×Rm) and on the local product Hardy space h1 (Rn ×Rm). We establish some boundedness criteria for Hausdorff operators on these function ...We study Hausdorff operators on the product Besov space B0,1 1 (Rn ×Rm) and on the local product Hardy space h1 (Rn ×Rm). We establish some boundedness criteria for Hausdorff operators on these function spaces.展开更多
In this article, we obtain the sharp bounds from LP(Gn) to the space wLP(Gn) for Hardy operators on product spaces. More generally, the precise norms of Hardy operators on product spaces from LP(Gn) to the space...In this article, we obtain the sharp bounds from LP(Gn) to the space wLP(Gn) for Hardy operators on product spaces. More generally, the precise norms of Hardy operators on product spaces from LP(Gn) to the space LPI (Gn) are obtained.展开更多
By means of vector-valued product Calderón-Zygmund operators and some subtle estimates,the boundedness in product Hardy spaces on R^n × R^m of Calderón-Zygmund operators introduced by J.L. Journé i...By means of vector-valued product Calderón-Zygmund operators and some subtle estimates,the boundedness in product Hardy spaces on R^n × R^m of Calderón-Zygmund operators introduced by J.L. Journé is established.展开更多
In this survey report, we shall mainly summarize some recent progress, interesting problems and typical methods used in the theory related to rough Marcinkiewicz integrals and rough singular integrals on product space...In this survey report, we shall mainly summarize some recent progress, interesting problems and typical methods used in the theory related to rough Marcinkiewicz integrals and rough singular integrals on product spaces. In addition, we give new proofs for some known results.展开更多
Via a series of orihogonal two-dimensional wavelets, an orthogonal decomposition of the space of square integral functions on Ux U (U is the upper half-plane) with the meaaure y_1^(_1) y_2~(_2 dx_1 dx_2 dy_1 dy_2 is g...Via a series of orihogonal two-dimensional wavelets, an orthogonal decomposition of the space of square integral functions on Ux U (U is the upper half-plane) with the meaaure y_1^(_1) y_2~(_2 dx_1 dx_2 dy_1 dy_2 is given. Four kinds of Toeplitz-Hankel type operators between the decomposition components are defined and boundedness. S_p properties of them are established.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 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.
In the paper we obtain vector-valued inequalities for Calderon-Zygmund operator, simply CZO on Herz space and weak Herz space. In particular, we obtain vector-valued inequalities for CZO on L^q(R^d,|x|^α d μ)spa...In the paper we obtain vector-valued inequalities for Calderon-Zygmund operator, simply CZO on Herz space and weak Herz space. In particular, we obtain vector-valued inequalities for CZO on L^q(R^d,|x|^α d μ)space, with 1〈q〈∞,-n〈α〈n(q-1),and on L^1,∞ (R^d,|x|^α d μ)space,with -n〈α〈0.展开更多
Let L1 and L2 be the Schrodinger operators on Rn and Rm, respectively. By using different maximal functions and Littlewood-Paley g function on distinct variables, in this paper,some characterizations for functions in ...Let L1 and L2 be the Schrodinger operators on Rn and Rm, respectively. By using different maximal functions and Littlewood-Paley g function on distinct variables, in this paper,some characterizations for functions in the product Hardy space HL1,L21(R^n×R^m) associated to operators L1 and L2 are obtained.展开更多
Making use of multivalent functions with negative coefficients of the type f (z)=z^(p)-~(∑)_(k=p+1)^(∞)a_(k)z^(k),which are analytic in the open unit disk and applying the q-derivative a q–differintegral operator i...Making use of multivalent functions with negative coefficients of the type f (z)=z^(p)-~(∑)_(k=p+1)^(∞)a_(k)z^(k),which are analytic in the open unit disk and applying the q-derivative a q–differintegral operator is considered.Furthermore by using the familiar Riesz-Dunford integral,a linear operator on Hilbert space H is introduced.A new subclass of p-valent functions related to an operator on H is defined.Coefficient estimate,distortion bound and extreme points are obtained.The convolution-preserving property is also investigated.展开更多
Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I (the identity operator). Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this pa...Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I (the identity operator). Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this paper, the boundedness of Tb on weighted Morrey space are obtained when b belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.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
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
To find the predual spaces Pα(R^n) of Qα(R^n) is an important motivation in the study of Q spaces. In this article, wavelet methods are used to solve this problem in a constructive way. First, an wavelet tent at...To find the predual spaces Pα(R^n) of Qα(R^n) is an important motivation in the study of Q spaces. In this article, wavelet methods are used to solve this problem in a constructive way. First, an wavelet tent atomic characterization of Pα(Rn) is given, then its usual atomic characterization and Poisson extension characterization are given. Finally, the continuity on Pα of Calderon-Zygmund operators is studied, and the result can be also applied to give the Morrey characterization of Pα(Rn).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
文摘For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.
基金Supported by the National Natural Science Foundation of China(10931001, 10871173 and 11026104)
文摘We study Hausdorff operators on the product Besov space B0,1 1 (Rn ×Rm) and on the local product Hardy space h1 (Rn ×Rm). We establish some boundedness criteria for Hausdorff operators on these function spaces.
基金supported by NSFC(11471309,11271162,and11561062)Project of Henan Provincial Department of Education(18A110028)+1 种基金the Nanhu Scholar Program for Young Scholars of XYNUDoctoral Scientific Research Startup Fund of Xinyang Normal University(2016)
文摘In this article, we obtain the sharp bounds from LP(Gn) to the space wLP(Gn) for Hardy operators on product spaces. More generally, the precise norms of Hardy operators on product spaces from LP(Gn) to the space LPI (Gn) are obtained.
基金supported by the National Natural Science Foundation of China(10871025)
文摘By means of vector-valued product Calderón-Zygmund operators and some subtle estimates,the boundedness in product Hardy spaces on R^n × R^m of Calderón-Zygmund operators introduced by J.L. Journé is established.
基金the Project of Development Plan of the State Key Fundamental Research Major Project of NNSFC,and NSFZJ.
文摘In this survey report, we shall mainly summarize some recent progress, interesting problems and typical methods used in the theory related to rough Marcinkiewicz integrals and rough singular integrals on product spaces. In addition, we give new proofs for some known results.
基金Research was supported by the National Natural Science Foundation of China.
文摘Via a series of orihogonal two-dimensional wavelets, an orthogonal decomposition of the space of square integral functions on Ux U (U is the upper half-plane) with the meaaure y_1^(_1) y_2~(_2 dx_1 dx_2 dy_1 dy_2 is given. Four kinds of Toeplitz-Hankel type operators between the decomposition components are defined and boundedness. S_p properties of them are established.
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 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.
文摘In the paper we obtain vector-valued inequalities for Calderon-Zygmund operator, simply CZO on Herz space and weak Herz space. In particular, we obtain vector-valued inequalities for CZO on L^q(R^d,|x|^α d μ)space, with 1〈q〈∞,-n〈α〈n(q-1),and on L^1,∞ (R^d,|x|^α d μ)space,with -n〈α〈0.
基金Supported by the National Natural Science Foundation of China(11471176)Natural Science Foundation of Shandong Province(BS2014SF002)
文摘Let L1 and L2 be the Schrodinger operators on Rn and Rm, respectively. By using different maximal functions and Littlewood-Paley g function on distinct variables, in this paper,some characterizations for functions in the product Hardy space HL1,L21(R^n×R^m) associated to operators L1 and L2 are obtained.
文摘Making use of multivalent functions with negative coefficients of the type f (z)=z^(p)-~(∑)_(k=p+1)^(∞)a_(k)z^(k),which are analytic in the open unit disk and applying the q-derivative a q–differintegral operator is considered.Furthermore by using the familiar Riesz-Dunford integral,a linear operator on Hilbert space H is introduced.A new subclass of p-valent functions related to an operator on H is defined.Coefficient estimate,distortion bound and extreme points are obtained.The convolution-preserving property is also investigated.
文摘Suppose T^k,l and T^k,2 are singular integrals with variable kernels and mixed homogeneity or ±I (the identity operator). Denote the Toeplitz type operator by T^b=k=1∑^QT^k,1M^bT^k,2 where M^bf= bf. In this paper, the boundedness of Tb on weighted Morrey space are obtained when b belongs to the weighted Lipschitz function space and weighted BMO function space, respectively.
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).
基金supported by NNSF of China No.10001027, 90104004,10471002973 project of China G1999075105+1 种基金the innovation funds of Wuhan Universitythe subject construction funds of Mathematic and Statistic School, Wuhan University.
文摘To find the predual spaces Pα(R^n) of Qα(R^n) is an important motivation in the study of Q spaces. In this article, wavelet methods are used to solve this problem in a constructive way. First, an wavelet tent atomic characterization of Pα(Rn) is given, then its usual atomic characterization and Poisson extension characterization are given. Finally, the continuity on Pα of Calderon-Zygmund operators is studied, and the result can be also applied to give the Morrey characterization of Pα(Rn).
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.