本文主要研究单位圆盘的Bergman空间上斜Toeplitz算子的交换性问题,利用Mellin变换得到以径向函数为符号的斜Toeplitz算子与解析斜Toeplitz算子可交换的一个必要条件,以及以特殊径向函数为符号的斜Toeplitz算子与解析斜Toeplitz算子可...本文主要研究单位圆盘的Bergman空间上斜Toeplitz算子的交换性问题,利用Mellin变换得到以径向函数为符号的斜Toeplitz算子与解析斜Toeplitz算子可交换的一个必要条件,以及以特殊径向函数为符号的斜Toeplitz算子与解析斜Toeplitz算子可交换的充要条件;并得到以函数azs+b| z |2t为符号的斜Toeplitz算子与解析斜Toeplitz算子可交换的充要条件。展开更多
本文给出调和Bergman空间上的斜Toeplitz算子和其衍生算子的概念,并介绍了衍生算子的积分表示、有界性和紧性。此有界性和紧性为后续研究斜Toeplitz算子的有界性和紧性提供了研究方法。In this paper, the concepts of slant Toeplitz o...本文给出调和Bergman空间上的斜Toeplitz算子和其衍生算子的概念,并介绍了衍生算子的积分表示、有界性和紧性。此有界性和紧性为后续研究斜Toeplitz算子的有界性和紧性提供了研究方法。In this paper, the concepts of slant Toeplitz operators and its derivative operators on harmonic Bergman Spaces are given, and the integral representation, boundness and compactness of the derivative operators are introduced. The boundedness and compactness provide a method for the subsequent studies of boundedness and compactness of slant Toeplitz operators.展开更多
The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic fu...The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic functions in the unit ball by radial derivative.Then we extend the Sharma's results.展开更多
研究了单位圆盘D上从加权Bergman空间到Hardy空间的Toeplitz算子,刻画了单位圆盘上p和q值不同时,从加权Bergman空间Aαp到Hardy空间Hp的Toeplitz算子的有界性和紧性。We study Toeplitz operators from weighted Bergman spaces to Hard...研究了单位圆盘D上从加权Bergman空间到Hardy空间的Toeplitz算子,刻画了单位圆盘上p和q值不同时,从加权Bergman空间Aαp到Hardy空间Hp的Toeplitz算子的有界性和紧性。We study Toeplitz operators from weighted Bergman spaces to Hardy spaces in the unit disk of D. We characterize the boundedness and compactness of Toeplitz operators from weighted Bergman spaces Aαpto Hardy spaces Hpfor the different values of p and q in the unit disk.展开更多
In this paper,it is shown that the harmonic Bergman projection P_(ω)^(h),induced by a radial,induced by a radial weightω,is bounded and onto from L^(∞)(D)to the harmonic Bloch space B_(h)if and only ifω∈D,,which ...In this paper,it is shown that the harmonic Bergman projection P_(ω)^(h),induced by a radial,induced by a radial weightω,is bounded and onto from L^(∞)(D)to the harmonic Bloch space B_(h)if and only ifω∈D,,which is a class of radial weights satisfying the two-sided doubling conditions.As an application,the bounded and compact positive Toeplitz operators T_(μ,ω)on the endpoint case weighted harmonic Bergman space L_(h,ω)^(1)(D)are characterized.展开更多
In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditio...In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.展开更多
文摘本文主要研究单位圆盘的Bergman空间上斜Toeplitz算子的交换性问题,利用Mellin变换得到以径向函数为符号的斜Toeplitz算子与解析斜Toeplitz算子可交换的一个必要条件,以及以特殊径向函数为符号的斜Toeplitz算子与解析斜Toeplitz算子可交换的充要条件;并得到以函数azs+b| z |2t为符号的斜Toeplitz算子与解析斜Toeplitz算子可交换的充要条件。
文摘本文给出调和Bergman空间上的斜Toeplitz算子和其衍生算子的概念,并介绍了衍生算子的积分表示、有界性和紧性。此有界性和紧性为后续研究斜Toeplitz算子的有界性和紧性提供了研究方法。In this paper, the concepts of slant Toeplitz operators and its derivative operators on harmonic Bergman Spaces are given, and the integral representation, boundness and compactness of the derivative operators are introduced. The boundedness and compactness provide a method for the subsequent studies of boundedness and compactness of slant Toeplitz operators.
基金Supported by Natural Science Foundation of Guangdong Province in China(2018KTSCX161)。
文摘The boundness and compactness of products of multiplication,composition and differentiation on weighted Bergman spaces in the unit ball are studied.We define the differentiation operator on the space of holomorphic functions in the unit ball by radial derivative.Then we extend the Sharma's results.
文摘研究了单位圆盘D上从加权Bergman空间到Hardy空间的Toeplitz算子,刻画了单位圆盘上p和q值不同时,从加权Bergman空间Aαp到Hardy空间Hp的Toeplitz算子的有界性和紧性。We study Toeplitz operators from weighted Bergman spaces to Hardy spaces in the unit disk of D. We characterize the boundedness and compactness of Toeplitz operators from weighted Bergman spaces Aαpto Hardy spaces Hpfor the different values of p and q in the unit disk.
基金supported by the National Natural Science Foundation of China(12171075)the Science and Technology Research Project of Education Department of Jilin Province(JJKH20241406KJ)Zhan’s research was supported by the Doctoral Startup Fund of Liaoning University of Technology(XB2024029).
文摘In this paper,it is shown that the harmonic Bergman projection P_(ω)^(h),induced by a radial,induced by a radial weightω,is bounded and onto from L^(∞)(D)to the harmonic Bloch space B_(h)if and only ifω∈D,,which is a class of radial weights satisfying the two-sided doubling conditions.As an application,the bounded and compact positive Toeplitz operators T_(μ,ω)on the endpoint case weighted harmonic Bergman space L_(h,ω)^(1)(D)are characterized.
基金supported by the National Natural Science Foundation of China(12171373)Chen's work also supported by the Fundamental Research Funds for the Central Universities of China(GK202207018).
文摘In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.
