In this paper,we characterize reverse Carleson measures for a class of generalized Fock spaces F^(p)_(φ),with 0<p<∞and withφsatisfying dd^(c)_(φ)■ω0.As an application of these results,we obtain several equ...In this paper,we characterize reverse Carleson measures for a class of generalized Fock spaces F^(p)_(φ),with 0<p<∞and withφsatisfying dd^(c)_(φ)■ω0.As an application of these results,we obtain several equivalent characterizations for invertible Toeplitz operators Tψ,induced by positive bounded symbols φ on F^(2)_(φ).展开更多
The present paper mainly gives some applications of Berezin type symbols on the Diriehlet space of unit ball. We study the solvability of some Riccati operator equations of the form XAX ＋ XB - CX = D related to harmo...The present paper mainly gives some applications of Berezin type symbols on the Diriehlet space of unit ball. We study the solvability of some Riccati operator equations of the form XAX ＋ XB - CX = D related to harmonic Toeplitz operators on the Dirichlet space. Especially, the invariant subspaces of Toeplitz operators are also considered.展开更多
In this paper,the authors investigate the boundedness of Toeplitz product T_(f)T_(g)and Hankel product H^(*)_(f)H_(g)on Fock-Sobolev space for f,g∈P.As a result,the boundedness of Toeplitz operator T_(f)and Hankel op...In this paper,the authors investigate the boundedness of Toeplitz product T_(f)T_(g)and Hankel product H^(*)_(f)H_(g)on Fock-Sobolev space for f,g∈P.As a result,the boundedness of Toeplitz operator T_(f)and Hankel operator H_(f)with f∈P is characterized.展开更多
In this paper,we introduce the work done on Hardy-Sobolev spaces and Fock-Sobolev spaces and their operators and operator algebras,including the study of boundedness,compactness,Fredholm property,index theory,spectrum...In this paper,we introduce the work done on Hardy-Sobolev spaces and Fock-Sobolev spaces and their operators and operator algebras,including the study of boundedness,compactness,Fredholm property,index theory,spectrum and essential spectrum,norm and essential norm,Schatten-p classes,and the C^(∗) algebras generated by them.展开更多
We discuss the Banach space structure of the fractional order weighted Fock-Sobolev spaces fPα,s, mainly include giving some growth estimates for Fock-Sobolev functions and approximating them by a sequence of ＇nice...We discuss the Banach space structure of the fractional order weighted Fock-Sobolev spaces fPα,s, mainly include giving some growth estimates for Fock-Sobolev functions and approximating them by a sequence of ＇nice＇ functions in two different ways.展开更多
基金supported by the NNSF of China(12071155)supported by the NNSF of China(11871170)+1 种基金the open project of Key Laboratory,school of Mathematical Sciences,Chongqing Normal University(CSSXKFKTM202002)supported by the Innovation Research for the Postgraduates of Guangzhou University(2020GDJC-D08)。
文摘In this paper,we characterize reverse Carleson measures for a class of generalized Fock spaces F^(p)_(φ),with 0<p<∞and withφsatisfying dd^(c)_(φ)■ω0.As an application of these results,we obtain several equivalent characterizations for invertible Toeplitz operators Tψ,induced by positive bounded symbols φ on F^(2)_(φ).
文摘The present paper mainly gives some applications of Berezin type symbols on the Diriehlet space of unit ball. We study the solvability of some Riccati operator equations of the form XAX ＋ XB - CX = D related to harmonic Toeplitz operators on the Dirichlet space. Especially, the invariant subspaces of Toeplitz operators are also considered.
基金supported by the National Natural Science Foundation of China(Nos.12071155,11871170)the Innovation Research for the Postgraduates of Guangzhou University(2020GDJCD08)
文摘In this paper,the authors investigate the boundedness of Toeplitz product T_(f)T_(g)and Hankel product H^(*)_(f)H_(g)on Fock-Sobolev space for f,g∈P.As a result,the boundedness of Toeplitz operator T_(f)and Hankel operator H_(f)with f∈P is characterized.
基金G.Cao was supported by the NNSF of China(Grant No.12071155)L.He was supported by the NNSF of China(Grant No.11871170).
文摘In this paper,we introduce the work done on Hardy-Sobolev spaces and Fock-Sobolev spaces and their operators and operator algebras,including the study of boundedness,compactness,Fredholm property,index theory,spectrum and essential spectrum,norm and essential norm,Schatten-p classes,and the C^(∗) algebras generated by them.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant Nos. 11501136, 11271092）, the Key Discipline Construction Project of Subject Groups Focus on Mathematics and Information Science in the Construction Project of the High-Level University of Guangdong Province （No. 4601-2015）, and the Project for the New Talent of Guangzhou University （No. HL02-1517）.
文摘We discuss the Banach space structure of the fractional order weighted Fock-Sobolev spaces fPα,s, mainly include giving some growth estimates for Fock-Sobolev functions and approximating them by a sequence of ＇nice＇ functions in two different ways.
