Some Problems Of Toeplitz Operators On The Analytic Function Space

In this thesis, we mainly study the Toeplitz operator on Fock space in Cn,and focus on the boundedness and compactness of the Toeplitz operator with positive sym-bols and determines when a Toeplitz operator Tμon Fock space in Cn belongs to the Schatten class.In chapter I. we discuss some related research background, and give some basic concepts and notations. At last, we show the significance of research work.In chapter 2, we characterize Carleson-type measures for Fock space in Cn and give several equivalent conditions for a positive Borel measure on Cn to be Fock-Carelson and vanishing Fock-Carelson.In chapter 3, we characterize the boundedness and compactness of the Toeplitz operator with positive symbols on Fock space in C" and obtain several equivalent con-ditions.In chapter 4, we determine when a Toeplitz operator Tμon Fock space in C" belongs to the Schatten class Sp.