In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends ...In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a group of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give some remarks derived from this study.展开更多
In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is ＂the generalized Neumann lemma＂...In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is ＂the generalized Neumann lemma＂ which is quite different from the method in [12] where ＂the generalized Banach lemma＂ was used. By the method of the perturba- tion analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.展开更多
In this paper,the authors consider theω-type Calder´on-Zygmund operator T_(ω)and the commutator[b,T_(ω)]generated by a symbol function b on the Lorentz space L^(p,r)(X)over the homogeneous space(X,d,μ).The bo...In this paper,the authors consider theω-type Calder´on-Zygmund operator T_(ω)and the commutator[b,T_(ω)]generated by a symbol function b on the Lorentz space L^(p,r)(X)over the homogeneous space(X,d,μ).The boundedness and the compactness of the commutator[b,T_(ω)]on Lorentz space L^(p,r)(X)are founded for any p∈(1,∞)and r∈[1,∞).展开更多
Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO（G） functions on Herz spaces in the setting of homogeneous group. This article ex...Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO（G） functions on Herz spaces in the setting of homogeneous group. This article extends some known results.展开更多
The authors establish the baundedness on homogeneous weighted Herz spaces for a large class of rough operators and their commutators with BMO functions. In particular, the Calderon-Zygmund singular integrals and the r...The authors establish the baundedness on homogeneous weighted Herz spaces for a large class of rough operators and their commutators with BMO functions. In particular, the Calderon-Zygmund singular integrals and the rough R. Fefferman singular integral operators and the rough Ricci-Stein oscillatory singular integrals and the corresponding commutators are considered.展开更多
We derive some strong type and weak type weighted norm estimates which re- late the commutators of potential integral operators to the corresponding maximal operators in the context of spaces of homogeneous type.
Let M α be the fractional maximal operators (0<α≤1) and (u,v) a pair of weight functions, u∈D ∞, σ=v~~~~^(-1/(p-1))∈A ∞. The boundedness of M α on some homogenous groups (G, ‖·‖, dx) and the cov...Let M α be the fractional maximal operators (0<α≤1) and (u,v) a pair of weight functions, u∈D ∞, σ=v~~~~^(-1/(p-1))∈A ∞. The boundedness of M α on some homogenous groups (G, ‖·‖, dx) and the covering Lemma of Calderon-Zygmund type are studied. Not only an adequate covering Lemma of Calderon-Zygmund type is shown, but also the boundedness of fractional maximal operators M α(0<α≤1) on some of homogeneous groups with respect to a given pair of weight functions (u,v) as above is proved. Moreover, a sufficient and necessary condition for M α∈B(u^qdx, v~~pdx), 0<α<1, 1<p<1α, and 1q=1p-α is also given. Finally, an application of the results is also obtained.展开更多
In this paper, the author computes the dimension of space of homogeneous Grushin-harmonic functions, and give an orthogonal basis of them. Moreover, the author describes the nodal curves of these homogenous Grushin-ha...In this paper, the author computes the dimension of space of homogeneous Grushin-harmonic functions, and give an orthogonal basis of them. Moreover, the author describes the nodal curves of these homogenous Grushin-harmonic basis. As an application of the orthogonal basis, the author proves a Liouville-type theorem for the Grushin operator, that is the Grushin-harmonic functions are homogeneous polynomials provided that the frequency of such a function is equal to some constant.展开更多
Weighted estimates with general weights are established for the maximal operator associated with the commutator generated by singular integral operator and BMO function on spaces of homogeneous type, where the associa...Weighted estimates with general weights are established for the maximal operator associated with the commutator generated by singular integral operator and BMO function on spaces of homogeneous type, where the associated kernel satisfies the HSlder condition on the first variable and some condition which is fairly weaker than the Holder condition on the second variable.展开更多
Let X be a space of homogeneous type with finite measure. Let T be a singular integral operator which is bounded on L^p （X）, 1 〈 p 〈 ∞. We give a sufficient condition on the kernel k（x,y） of Tso thatwhen a func...Let X be a space of homogeneous type with finite measure. Let T be a singular integral operator which is bounded on L^p （X）, 1 〈 p 〈 ∞. We give a sufficient condition on the kernel k（x,y） of Tso thatwhen a function b ∈ BMO （X）,the commutator [b,T] （f）=T （b f）- bT （f） is bounded on spaces L^p for all p, 1 〈 p 〈 ∞.展开更多
We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit p...We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient conditions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide ＂computable＂ estimates on the operator norm.展开更多
Let Φ be a Young function and MΦ be the maximal operator associated with Φ in the space of homogeneous type.In this paper,the composition of the maximal operators of type MΦ is considered,and the result establishe...Let Φ be a Young function and MΦ be the maximal operator associated with Φ in the space of homogeneous type.In this paper,the composition of the maximal operators of type MΦ is considered,and the result established by Carrozza and Passarelli Di Napoli[2] is generalized to the space of homogeneous type.展开更多
We obtain weak type （1, q） inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces. The proofs use some properties of maximal operators. Our results are closely related to the str...We obtain weak type （1, q） inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces. The proofs use some properties of maximal operators. Our results are closely related to the strong type inequalities in [13, 14, 15].展开更多
In this paper,pseudo-differential operators with homogeneous symbol classes associated with the Weinstein transform are introduced.The boundedness of pseudo-differential operators and commutator between two pseudo-dif...In this paper,pseudo-differential operators with homogeneous symbol classes associated with the Weinstein transform are introduced.The boundedness of pseudo-differential operators and commutator between two pseudo-differential operators on H_(α,2)^(r) are proven with the help of the Weinstein transform technique.展开更多
In this note, the author introduces some new subcIasses of starlike mappings S^＊Ωn1p2,…,pn（β,A,B）={f∈H（Ω）：｜itanβ＋（1-itanβ）2/p（z）аp/аz（z）Jf^-1（z）f（z）-1-AB/1-B^2｜〈B-A/1-B^2},on Reinhardt dom...In this note, the author introduces some new subcIasses of starlike mappings S^＊Ωn1p2,…,pn（β,A,B）={f∈H（Ω）：｜itanβ＋（1-itanβ）2/p（z）аp/аz（z）Jf^-1（z）f（z）-1-AB/1-B^2｜〈B-A/1-B^2},on Reinhardt domains Ωn1p2,…,pn=z∈C^n：｜z1｜^2＋n∑j=2｜zj｜^pj〈1}where - 1≤A〈B〈1,q=min{p2,…,pn}≥1,l=max{p2,…,pn}≥2 and β ∈（-π/2,π/2）.Some different conditions for P are established such that these classes are preserved under the following modified Roper-Suffridge operator F（z）=（f（z1）＋f＇（z1）Pm（z0）,（f＇（z1））^1/mz0）＇where f is a normalized biholomorphic function on the unit disc D, z = （z1,z0） ∈Ωn1p2,…,pn,z0=（z2,…,zn）∈ C^n-1.Another condition for P is also obtained such that the above generalized Roper-Suffridge operator preserves an almost spirallike function of type/3 and order β These results generalize the modified Roper-Suffridge extension oper-ator from the unit ball to Reinhardt domains. Notice that when p2 = p3 …=pn = 2,our results reduce to the recent results of Feng and Yu.展开更多
LP(Rn) boundedness is considered for the multilinear singular integral operator defined by where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one. A has derivatives...LP(Rn) boundedness is considered for the multilinear singular integral operator defined by where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one. A has derivatives of order one in BMO(Rn). We give a smoothness condition which is fairly weaker than that Ω∈Lipαt(Sn-1) (0 <α≤1) and implies the LP(Rn) (1 < p <∞) boundedness for the operator TA.Some endpoint estimates are also established.展开更多
文摘In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a group of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give some remarks derived from this study.
基金Supported by the Nature Science Foundation of China(11471091 and 11401143)
文摘In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is ＂the generalized Neumann lemma＂ which is quite different from the method in [12] where ＂the generalized Banach lemma＂ was used. By the method of the perturba- tion analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.
基金supported by the NNSF of China(12271483,11961056)the NSF of Jiangxi Province(20192BAB201004)+1 种基金supported by the“Xin-Miao”Program of Zhejiang Province(2021R415027)the Innovation Fund of ZUST(2020yjskc06).
文摘In this paper,the authors consider theω-type Calder´on-Zygmund operator T_(ω)and the commutator[b,T_(ω)]generated by a symbol function b on the Lorentz space L^(p,r)(X)over the homogeneous space(X,d,μ).The boundedness and the compactness of the commutator[b,T_(ω)]on Lorentz space L^(p,r)(X)are founded for any p∈(1,∞)and r∈[1,∞).
基金Supported by Chinese Universities Scientific Fund(2009RC0703 of BUPT)the NNSF of China (10871024)
文摘Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO（G） functions on Herz spaces in the setting of homogeneous group. This article extends some known results.
基金Project 19871071 supported by Natural Science Foundation of China
文摘The authors establish the baundedness on homogeneous weighted Herz spaces for a large class of rough operators and their commutators with BMO functions. In particular, the Calderon-Zygmund singular integrals and the rough R. Fefferman singular integral operators and the rough Ricci-Stein oscillatory singular integrals and the corresponding commutators are considered.
基金Supported by the National Natural Science Foundation of China(Nos.10771049, 60773174)the Natural Science Foundation of Hebei Province (08M001)
文摘We derive some strong type and weak type weighted norm estimates which re- late the commutators of potential integral operators to the corresponding maximal operators in the context of spaces of homogeneous type.
文摘Let M α be the fractional maximal operators (0<α≤1) and (u,v) a pair of weight functions, u∈D ∞, σ=v~~~~^(-1/(p-1))∈A ∞. The boundedness of M α on some homogenous groups (G, ‖·‖, dx) and the covering Lemma of Calderon-Zygmund type are studied. Not only an adequate covering Lemma of Calderon-Zygmund type is shown, but also the boundedness of fractional maximal operators M α(0<α≤1) on some of homogeneous groups with respect to a given pair of weight functions (u,v) as above is proved. Moreover, a sufficient and necessary condition for M α∈B(u^qdx, v~~pdx), 0<α<1, 1<p<1α, and 1q=1p-α is also given. Finally, an application of the results is also obtained.
基金supported by National Natural Science Foundation of China(11401310)Natural Science Foundation of Jiangsu Province(BK20140965)+2 种基金High level talent research fund of Nanjing Forestry University(G2014022)supported by the overseas research program of Jiangsu Provincesponsored by Qing Lan Project of Jiangsu Province
文摘In this paper, the author computes the dimension of space of homogeneous Grushin-harmonic functions, and give an orthogonal basis of them. Moreover, the author describes the nodal curves of these homogenous Grushin-harmonic basis. As an application of the orthogonal basis, the author proves a Liouville-type theorem for the Grushin operator, that is the Grushin-harmonic functions are homogeneous polynomials provided that the frequency of such a function is equal to some constant.
文摘Weighted estimates with general weights are established for the maximal operator associated with the commutator generated by singular integral operator and BMO function on spaces of homogeneous type, where the associated kernel satisfies the HSlder condition on the first variable and some condition which is fairly weaker than the Holder condition on the second variable.
基金Supported by the National Natural Science Foundation of China
文摘Let X be a space of homogeneous type with finite measure. Let T be a singular integral operator which is bounded on L^p （X）, 1 〈 p 〈 ∞. We give a sufficient condition on the kernel k（x,y） of Tso thatwhen a function b ∈ BMO （X）,the commutator [b,T] （f）=T （b f）- bT （f） is bounded on spaces L^p for all p, 1 〈 p 〈 ∞.
文摘We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient conditions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide ＂computable＂ estimates on the operator norm.
基金Supported by the NSF from the Education Department of Henan Province(2007110006)
文摘Let Φ be a Young function and MΦ be the maximal operator associated with Φ in the space of homogeneous type.In this paper,the composition of the maximal operators of type MΦ is considered,and the result established by Carrozza and Passarelli Di Napoli[2] is generalized to the space of homogeneous type.
基金Supported by Fundamental Research Program 2011-2012
文摘We obtain weak type （1, q） inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces. The proofs use some properties of maximal operators. Our results are closely related to the strong type inequalities in [13, 14, 15].
基金Supported by SERB MATRICS(Grant No.MTR2021/000266)。
文摘In this paper,pseudo-differential operators with homogeneous symbol classes associated with the Weinstein transform are introduced.The boundedness of pseudo-differential operators and commutator between two pseudo-differential operators on H_(α,2)^(r) are proven with the help of the Weinstein transform technique.
基金supported by the National Natural Science Foundation of China(11001246,11101139)Zhejiang Innovation Project(T200905)
文摘In this note, the author introduces some new subcIasses of starlike mappings S^＊Ωn1p2,…,pn（β,A,B）={f∈H（Ω）：｜itanβ＋（1-itanβ）2/p（z）аp/аz（z）Jf^-1（z）f（z）-1-AB/1-B^2｜〈B-A/1-B^2},on Reinhardt domains Ωn1p2,…,pn=z∈C^n：｜z1｜^2＋n∑j=2｜zj｜^pj〈1}where - 1≤A〈B〈1,q=min{p2,…,pn}≥1,l=max{p2,…,pn}≥2 and β ∈（-π/2,π/2）.Some different conditions for P are established such that these classes are preserved under the following modified Roper-Suffridge operator F（z）=（f（z1）＋f＇（z1）Pm（z0）,（f＇（z1））^1/mz0）＇where f is a normalized biholomorphic function on the unit disc D, z = （z1,z0） ∈Ωn1p2,…,pn,z0=（z2,…,zn）∈ C^n-1.Another condition for P is also obtained such that the above generalized Roper-Suffridge operator preserves an almost spirallike function of type/3 and order β These results generalize the modified Roper-Suffridge extension oper-ator from the unit ball to Reinhardt domains. Notice that when p2 = p3 …=pn = 2,our results reduce to the recent results of Feng and Yu.
文摘LP(Rn) boundedness is considered for the multilinear singular integral operator defined by where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one. A has derivatives of order one in BMO(Rn). We give a smoothness condition which is fairly weaker than that Ω∈Lipαt(Sn-1) (0 <α≤1) and implies the LP(Rn) (1 < p <∞) boundedness for the operator TA.Some endpoint estimates are also established.
