We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.
In this paper, linear combinations of composition operators acting on weighted Dirichlet spaces are studied. By using the first derivative of the kernel function, we obtain a lower estimate for the essential norms of ...In this paper, linear combinations of composition operators acting on weighted Dirichlet spaces are studied. By using the first derivative of the kernel function, we obtain a lower estimate for the essential norms of these operators acting on the Dirichlet space D and S2. For general weighted Dirichlet space, by using complex interpolation methods, we characterize the compactness of these operators induced by linear fractional self-maps of the disk.展开更多
The Carleson measures for weighted Dirichlet spaces had been characterized by Girela and Peláez,who also characterized the boundedness of Volterra type operators between weighted Dirichlet spaces.However,their ch...The Carleson measures for weighted Dirichlet spaces had been characterized by Girela and Peláez,who also characterized the boundedness of Volterra type operators between weighted Dirichlet spaces.However,their characterizations for the boundedness are not complete.In this paper,the author completely characterizes the boundedness and compactness of Volterra type operators from the weighted Dirichlet spaces D^(p)_(α)to _(Dβ)^(q)(-1<α,βand 0<p<q<∞),which essentially complete their works.Furthermore,the author investigates the order boundedness of Volterra type operators between weighted Dirichlet spaces.展开更多
The family of spaces F(p,q,s)was introduced by the author in 1996.Since then,there has been great development in the theory of these spaces,due to the fact that these spaces include many classical function spaces,and ...The family of spaces F(p,q,s)was introduced by the author in 1996.Since then,there has been great development in the theory of these spaces,due to the fact that these spaces include many classical function spaces,and have connections with many other areas of mathematics.In this survey we present some basic properties and recent results on F(p,q,s)spaces.展开更多
In this paper, we study the boundedness of the generalized Cesàro operator on the weighted Dirichlet spaces Dα={f∈H（D）;‖f‖Dα^2=｜f（0）｜^2＋∫D｜f＇（z）｜^2（1-｜z｜^αdm（z）〈＋∞},where -1 〈 α 〈＋...In this paper, we study the boundedness of the generalized Cesàro operator on the weighted Dirichlet spaces Dα={f∈H（D）;‖f‖Dα^2=｜f（0）｜^2＋∫D｜f＇（z）｜^2（1-｜z｜^αdm（z）〈＋∞},where -1 〈 α 〈＋∞ and H（D） is the class of all holomorphic functions on the unit disc D.展开更多
Let p>0 andνbe a normal function on[0,1).In this paper,several equivalent characterizations are given for which composition operators are bounded or compact on the normal weight Dirichlet type space D_(ν)^(p)(D)i...Let p>0 andνbe a normal function on[0,1).In this paper,several equivalent characterizations are given for which composition operators are bounded or compact on the normal weight Dirichlet type space D_(ν)^(p)(D)in the unit disc.展开更多
基金This work was supported by NSF of China(11171203,11201280)New Teacher’s Fund for Doctor Stations,Ministry of Education(20114402120003)NSF of Guangdong Province(10151503101000025,S2011010004511,S2011040004131)
文摘We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.
文摘In this paper, linear combinations of composition operators acting on weighted Dirichlet spaces are studied. By using the first derivative of the kernel function, we obtain a lower estimate for the essential norms of these operators acting on the Dirichlet space D and S2. For general weighted Dirichlet space, by using complex interpolation methods, we characterize the compactness of these operators induced by linear fractional self-maps of the disk.
基金supported by the National Natural Science Foundation of China(No.11801094)。
文摘The Carleson measures for weighted Dirichlet spaces had been characterized by Girela and Peláez,who also characterized the boundedness of Volterra type operators between weighted Dirichlet spaces.However,their characterizations for the boundedness are not complete.In this paper,the author completely characterizes the boundedness and compactness of Volterra type operators from the weighted Dirichlet spaces D^(p)_(α)to _(Dβ)^(q)(-1<α,βand 0<p<q<∞),which essentially complete their works.Furthermore,the author investigates the order boundedness of Volterra type operators between weighted Dirichlet spaces.
文摘The family of spaces F(p,q,s)was introduced by the author in 1996.Since then,there has been great development in the theory of these spaces,due to the fact that these spaces include many classical function spaces,and have connections with many other areas of mathematics.In this survey we present some basic properties and recent results on F(p,q,s)spaces.
基金the National Natural Science Foundation of China (10471039) the Natural Science Foundation of Zhejiang Province (103104)the Natural Science Foundation of Huzhou City (2005YZ02)the Foundation of Huzhou Teachers'College (KX21030)
文摘In this paper, we study the boundedness of the generalized Cesàro operator on the weighted Dirichlet spaces Dα={f∈H（D）;‖f‖Dα^2=｜f（0）｜^2＋∫D｜f＇（z）｜^2（1-｜z｜^αdm（z）〈＋∞},where -1 〈 α 〈＋∞ and H（D） is the class of all holomorphic functions on the unit disc D.
基金supported by the National Natural Science Foundation of China(Grant No.11942109).
文摘Let p>0 andνbe a normal function on[0,1).In this paper,several equivalent characterizations are given for which composition operators are bounded or compact on the normal weight Dirichlet type space D_(ν)^(p)(D)in the unit disc.
