Schatten Class Membership Of Toeplitz Operators On Fock Space Of C~n

This dissertation investigates Schatten class membership of Toeplitz operators Tμ on Fock space Fα2(dva).We fix a positive parameter a and define the Gaussion measure as follows: If μ is a positive Borel measure,we define Toeplitz operator Tμ as follows:Because Fock spaces, Bergman spaces and Hilbert spaces are closely linked, the methods and techniques that we use while researching linear operators’properties on these spaces are similary. Basing on the research results of Toeplitz operators on Fock space in the complex plane, we utilize the basic properties of the Schatten class on Hilbert space, and use the Fock-Carleson measure, Berezin transform, the property of lattice and the average function to get the necessary and sufficient conditions of Tμ belonging to Schatten class.This thesis contains two chapters. In the first chapter, we gives the research background and the research situation, which introduce the development process of Toeplitz operators and some research results, and then gives the main conclusion-s. The second chapter contains four sections. The first and second section mainly gives some definitions, notations needed in this paper, and the basic lemmas required in the processions of proving main theorems. The third section mainly discusses the Toeplitz operator in Sp when p≥1. The fourth section mainly discusses the Toeplitz operator in Sp when0<p≤1. This thesis’s main results are theorem2.3.1and theorem2.4.1.