Operators on the orthogonal complement of the Dirichlet space (Ⅱ)

查看全文 作　　者：YU [1]Tao

机构地区：[1]Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

出　　处：《Science China Mathematics》索引2011年第54卷第9期,共8页

基　　金：supported by National Natural Science Foundation of China (Grant Nos.10971195 and 10771064);Natural Science Foundation of Zhejiang Province (Grant Nos. Y6090689 and Y6110260);Zhejiang Innovation Project (Grant No. T200905) 摘　　要：In this paper we first prove that a dual Hankel operator R φ on the orthogonal complement of the Dirichlet space is compact for φ∈ W 1,∞(D),and then that a semicommutator of two Toeplitz operators on the Dirichlet space or two dual Toeplitz operators on the orthogonal complement of the Dirichlet space in Sobolev space is compact.We also prove that a dual Hankel operator R φ with φ∈ W 1,∞(D) is of finite rank if and only if B φ is orthogonal to the Dirichlet space for some finite Blaschke product B,and give a sufficient and necessary condition for the semicommutator of two dual Toeplitz operators to be of finite rank. 关键词：DIRICHLET空间正交补 TOEPLITZ算子运算符 SOBOLEV空间 HANKEL 充分必要条件证明

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Operators on the orthogonal complement of the Dirichlet space (Ⅱ)

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