In this paper,by lifting the Bergman shift as the compression of an isometry on a subspace of the Hardy space of the bidisk,we give a proof of the Beurling type theorem on the Bergman space of Aleman,Richter and Sundb...In this paper,by lifting the Bergman shift as the compression of an isometry on a subspace of the Hardy space of the bidisk,we give a proof of the Beurling type theorem on the Bergman space of Aleman,Richter and Sundberg(1996) via the Hardy space of the bidisk.展开更多
We give a new and simple compactness condition for composition operators on BMOA,the space of all analytic functions of the bounded mean oscillation on the unit disk.Using our results one may immediately obtain that c...We give a new and simple compactness condition for composition operators on BMOA,the space of all analytic functions of the bounded mean oscillation on the unit disk.Using our results one may immediately obtain that compactness of a composition operator on BMOA implies its compactness on the Bloch space as well as on the Hardy space.Similar results on VMOA are also given.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 10871083)National Science Foundation of USA (Grant No. 0457285)
文摘In this paper,by lifting the Bergman shift as the compression of an isometry on a subspace of the Hardy space of the bidisk,we give a proof of the Beurling type theorem on the Bergman space of Aleman,Richter and Sundberg(1996) via the Hardy space of the bidisk.
基金This work was partially supported by the Research Foundation for Doctor Programme(Grant No.20060560002)the National Natural Science Foundation of China(Grant No.10671115)
文摘We give a new and simple compactness condition for composition operators on BMOA,the space of all analytic functions of the bounded mean oscillation on the unit disk.Using our results one may immediately obtain that compactness of a composition operator on BMOA implies its compactness on the Bloch space as well as on the Hardy space.Similar results on VMOA are also given.
