Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting...Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.展开更多
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
In this paper, we give a necessary and sufficient condition for weighted composition operators Cu,φ to be boundedness on Bloch type spaces B^α. The theorem generalizes some previous results.
In this article, we borrow the idea of using Schur＇s test to characterize the compactness of composition operators on the weighted Bergman spaces in a bounded symmetricdomain Ω and verify that Cφ is compact on Lqa...In this article, we borrow the idea of using Schur＇s test to characterize the compactness of composition operators on the weighted Bergman spaces in a bounded symmetricdomain Ω and verify that Cφ is compact on Lqa（Ω,dvβ）if and only if K（φ（z）,φ（z））/K（z,z）→0 as z→ Ω under a mild condition,where K（z,w）is the Bergman kernel.展开更多
On bounded symmetric domain Ω of C^n, we investigate the properties of functions in weighted Bergman spaces A^P（Ω,dvs） for 0 〈 p ≤ ＋∞ and -1 〈 s 〈 4-∞. Based on the estimate of Bergman kernel, we obtain som...On bounded symmetric domain Ω of C^n, we investigate the properties of functions in weighted Bergman spaces A^P（Ω,dvs） for 0 〈 p ≤ ＋∞ and -1 〈 s 〈 4-∞. Based on the estimate of Bergman kernel, we obtain some characterizations of functions in A^P（Ω, dvs） in terms of a class of linear operators D^αB. Making use of these characterizations, we extend A^P（Ω,dvs） to the weighted Bergman spaces Aα^p,B（Ω,dvs） in a very natural way for 1 〈 p 〈 4-∞ and any real number s, that is, -∞ 〈 s 〈 ＋∞. This unified treatment covers some classical Bergman spaces, Besov spaces and Bloch spaces. Meanwhile, the boundedness of Bergman projection operators on Aα^P,β（Ω, dvs） and the dual of Aα^P,B（Ω, dvs） are given.展开更多
In this paper, we give a criterion of the absolutely Cesàro bounded weighted backward shift in spirit of the comparison method. Our approach is to construct the proper product of weight functions <img src=&quo...In this paper, we give a criterion of the absolutely Cesàro bounded weighted backward shift in spirit of the comparison method. Our approach is to construct the proper product of weight functions <img src="Edit_7232e0dc-07ab-41c5-8657-a49f0463b47c.bmp" alt="" />by the fraction of two monomials of the indexes, then we apply proper scaling to give Cesàro boundedness. In particular, we present a new example of non Cesàro bounded weighted backward shift on <img src="Edit_799dadb7-40ab-48f9-bae3-191378f96164.bmp" alt="" />.展开更多
In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exac...In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are different counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.展开更多
In this paper we consider operators with endpoint singularities generated by linear fractional Carleman shift in weighted Hölder spaces. Such operators play an important role in the study of algebras generate...In this paper we consider operators with endpoint singularities generated by linear fractional Carleman shift in weighted Hölder spaces. Such operators play an important role in the study of algebras generated by the operators of singular integration and multiplication by function. For the considered operators, we obtained more precise relations between norms of integral operators with local singularities in weighted Lebesgue spaces and norms in weighted Hölder spaces, making use of previously obtained general results. We prove the boundedness of operators with linear fractional singularities.展开更多
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
Let BE be a bounded symmetric domain realized as the unit open ball of JB^(*)-triples.The authors will characterize the bounded weighted composition operator from the Bloch space B(BE)to weighted Hardy space Hv∞in te...Let BE be a bounded symmetric domain realized as the unit open ball of JB^(*)-triples.The authors will characterize the bounded weighted composition operator from the Bloch space B(BE)to weighted Hardy space Hv∞in terms of Kobayashi distance.The authors also give a sufficient condition for the compactness,and also give the upper bound of its essential norm.As a corollary,they show that the boundedness and compactness are equivalent for composition operator fromB(BE)to H∞(BE),when is a finite dimension JB^(*)-triple.Finally,they show the boundedness and compactness of weighted composition operators from B(BE)to Hv,0∞(BE)are equivalent when is a finite dimension JB^(*)-triple.展开更多
We study the weighted composition operators Wh,on Hardy space H2（B） whenever h ∈ BMOA（resp.h ∈ VMOA）.Analogous results are given for Hp（B） spaces and the scale of weighted Bergman spaces.In the latter case,BMO...We study the weighted composition operators Wh,on Hardy space H2（B） whenever h ∈ BMOA（resp.h ∈ VMOA）.Analogous results are given for Hp（B） spaces and the scale of weighted Bergman spaces.In the latter case,BMOA is replaced by the Bloch space（resp.VMOA by the little Bloch space）.展开更多
Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequali...Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space.展开更多
The main purpose of this paper is to investigate the properties of the higher order commutators of maximal Calderón-Zygmund operators with Dini-type kernels.Two weighted estimates have been established for these ...The main purpose of this paper is to investigate the properties of the higher order commutators of maximal Calderón-Zygmund operators with Dini-type kernels.Two weighted estimates have been established for these commutators.Similar results have also been extended to multilinear setting.展开更多
The purpose of this paper is to study the composition operators on weightedBergman spaces of bounded symmetric domains.The sufficient and necessary conditions for a composition operator C"to be bounded add corn p...The purpose of this paper is to study the composition operators on weightedBergman spaces of bounded symmetric domains.The sufficient and necessary conditions for a composition operator C"to be bounded add corn pact respectively are given in term of the concept of Carleson measure.Meanwhile,the integral characteristic of n such that Cn is a Schatten p-class operator is obtained.展开更多
In this paper we consider the Nemytskii operator, i.e., the composition operator defined by (Nf)(t)=H(t,f(t)), where H is a given set-valued function. It is shown that if the operator N maps the space of functions bou...In this paper we consider the Nemytskii operator, i.e., the composition operator defined by (Nf)(t)=H(t,f(t)), where H is a given set-valued function. It is shown that if the operator N maps the space of functions bounded φ1-variation in the sense of Riesz with respect to the weight function αinto the space of set-valued functions of bounded φ2-variation in the sense of Riesz with respect to the weight, if it is globally Lipschitzian, then it has to be of the form (Nf)(t)=A(t)f(t)+B(t), where A(t) is a linear continuous set-valued function and B is a set-valued function of bounded φ2-variation in the sense of Riesz with respect to the weight.展开更多
In this paper,necessary and sufficient conditions are given for the weighted composition operator T_(ψ,ψ) to be bounded or compact from the space β_μ to β_ν (or β_(μ,0) to β_(ν,0) ) on the unit ball of C^n.A...In this paper,necessary and sufficient conditions are given for the weighted composition operator T_(ψ,ψ) to be bounded or compact from the space β_μ to β_ν (or β_(μ,0) to β_(ν,0) ) on the unit ball of C^n.At the same time,a series of corollaries are also obtained.展开更多
文摘Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.
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the Scientific Research Program of the Higher Education Institution of Xinjiang(XJEDU2005E06)
文摘In this paper, we give a necessary and sufficient condition for weighted composition operators Cu,φ to be boundedness on Bloch type spaces B^α. The theorem generalizes some previous results.
基金Supported by the National Natural Science Foundation of China (10771064)Natural Science Foundation of Zhejiang Province (Y7080197, Y6090036, Y6100219)+1 种基金Foundation of Creative Group in Colleges and Universities of Zhejiang Province (T200924)Foundation of Department of Education of Zhejiang province (20070482)
文摘In this article, we borrow the idea of using Schur＇s test to characterize the compactness of composition operators on the weighted Bergman spaces in a bounded symmetricdomain Ω and verify that Cφ is compact on Lqa（Ω,dvβ）if and only if K（φ（z）,φ（z））/K（z,z）→0 as z→ Ω under a mild condition,where K（z,w）is the Bergman kernel.
基金the NNSF of China(10571164)the SRFDP of Higher Education(20050358052)
文摘On bounded symmetric domain Ω of C^n, we investigate the properties of functions in weighted Bergman spaces A^P（Ω,dvs） for 0 〈 p ≤ ＋∞ and -1 〈 s 〈 4-∞. Based on the estimate of Bergman kernel, we obtain some characterizations of functions in A^P（Ω, dvs） in terms of a class of linear operators D^αB. Making use of these characterizations, we extend A^P（Ω,dvs） to the weighted Bergman spaces Aα^p,B（Ω,dvs） in a very natural way for 1 〈 p 〈 4-∞ and any real number s, that is, -∞ 〈 s 〈 ＋∞. This unified treatment covers some classical Bergman spaces, Besov spaces and Bloch spaces. Meanwhile, the boundedness of Bergman projection operators on Aα^P,β（Ω, dvs） and the dual of Aα^P,B（Ω, dvs） are given.
文摘In this paper, we give a criterion of the absolutely Cesàro bounded weighted backward shift in spirit of the comparison method. Our approach is to construct the proper product of weight functions <img src="Edit_7232e0dc-07ab-41c5-8657-a49f0463b47c.bmp" alt="" />by the fraction of two monomials of the indexes, then we apply proper scaling to give Cesàro boundedness. In particular, we present a new example of non Cesàro bounded weighted backward shift on <img src="Edit_799dadb7-40ab-48f9-bae3-191378f96164.bmp" alt="" />.
基金supported by the National Natural Science Foundation of China (10901158)
文摘In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are different counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.
文摘In this paper we consider operators with endpoint singularities generated by linear fractional Carleman shift in weighted Hölder spaces. Such operators play an important role in the study of algebras generated by the operators of singular integration and multiplication by function. For the considered operators, we obtained more precise relations between norms of integral operators with local singularities in weighted Lebesgue spaces and norms in weighted Hölder spaces, making use of previously obtained general results. We prove the boundedness of operators with linear fractional singularities.
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 the National Natural Science Foundation of China(No.12171251)。
文摘Let BE be a bounded symmetric domain realized as the unit open ball of JB^(*)-triples.The authors will characterize the bounded weighted composition operator from the Bloch space B(BE)to weighted Hardy space Hv∞in terms of Kobayashi distance.The authors also give a sufficient condition for the compactness,and also give the upper bound of its essential norm.As a corollary,they show that the boundedness and compactness are equivalent for composition operator fromB(BE)to H∞(BE),when is a finite dimension JB^(*)-triple.Finally,they show the boundedness and compactness of weighted composition operators from B(BE)to Hv,0∞(BE)are equivalent when is a finite dimension JB^(*)-triple.
基金Supported by National Natural Science Foundation of China(Grant No.10971040)
文摘We study the weighted composition operators Wh,on Hardy space H2（B） whenever h ∈ BMOA（resp.h ∈ VMOA）.Analogous results are given for Hp（B） spaces and the scale of weighted Bergman spaces.In the latter case,BMOA is replaced by the Bloch space（resp.VMOA by the little Bloch space）.
基金Supported by Guangdong Basic and Applied Basic Research Foundation(Grant No.2022A1515012429)Guangzhou Huashang College Research Team Project(Grant No.2021HSKT03)。
文摘Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space.
文摘The main purpose of this paper is to investigate the properties of the higher order commutators of maximal Calderón-Zygmund operators with Dini-type kernels.Two weighted estimates have been established for these commutators.Similar results have also been extended to multilinear setting.
文摘The purpose of this paper is to study the composition operators on weightedBergman spaces of bounded symmetric domains.The sufficient and necessary conditions for a composition operator C"to be bounded add corn pact respectively are given in term of the concept of Carleson measure.Meanwhile,the integral characteristic of n such that Cn is a Schatten p-class operator is obtained.
文摘In this paper we consider the Nemytskii operator, i.e., the composition operator defined by (Nf)(t)=H(t,f(t)), where H is a given set-valued function. It is shown that if the operator N maps the space of functions bounded φ1-variation in the sense of Riesz with respect to the weight function αinto the space of set-valued functions of bounded φ2-variation in the sense of Riesz with respect to the weight, if it is globally Lipschitzian, then it has to be of the form (Nf)(t)=A(t)f(t)+B(t), where A(t) is a linear continuous set-valued function and B is a set-valued function of bounded φ2-variation in the sense of Riesz with respect to the weight.
基金supported by the Foundation of Education Department of Hunan Province(Grant No.04C328)the Natrual Science Foundation of Zhejiang Province(Grant Nos.M103104&Y604569)the Science and Technology Foundation of Education Department of China(Grant No,204063).
文摘In this paper,necessary and sufficient conditions are given for the weighted composition operator T_(ψ,ψ) to be bounded or compact from the space β_μ to β_ν (or β_(μ,0) to β_(ν,0) ) on the unit ball of C^n.At the same time,a series of corollaries are also obtained.
