Fock-Sobolev Space And Dual Toeplitz Operator On Its Orthogonal Complement

In this thesis,we discuss the dual Toeplitz operator on the orthogonal complement of multi-dimensional Fock-Sobolev space.The Pseudo-Carleson measure and the vanishing Pseudo-Carleson measure in Fock-Sobolev space are defined.The equivalent conditions are given that the complex Borel measure on Fock-Sobolev space is Pseudo-Carleson measure and the vanishing Pseudo-Carleson measure.The boundedness and compactness of dual Toeplitz operators on the Fock-Sobolev space are described.In chapter 1,the related research background of dual Toeplitz operator are introduced,as well as some basic notations,preliminary knowledge and main results of this thesis.In chapter 2,the equivalent conditions of the Pseudo-Carleson measure and the vanishing Pseudo-Carleson measure for the complex Borel measure on FockSobolev space are studied by estimating the reproducing kernel of the Fock-Sobolev space.In chapter 3,the necessary and su cient conditions for the boundedness and compactness of dual Toeplitz operator for the orthogonal complement of the FockSobolev space are introduced.