In this paper we first prove that a dual Hankel operator Rφ 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 Dirich...In this paper we first prove that a dual Hankel operator Rφ 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 Re with φ ∈ W^1,∞（D） is of finite rank if and only if Be 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.展开更多
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)
文摘In this paper we first prove that a dual Hankel operator Rφ 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 Re with φ ∈ W^1,∞（D） is of finite rank if and only if Be 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.
