Operator Theory On Two Types Of Fock Spaces

In this paper,we characterize the positive Borel measure ? on C for which the induced Toeplitz operator T_? is bounded(or compact)between one doubling Fock spaceF~p(?)and another F~?(?).Moreover,We also discuss the boundedness and compactness of the opertor on the Fock-Sobolev spaceF_?~2.In chapter 1,We introduce the history and the development process of the operator theory involved on the two kinds of Fock spaces,and give the prerequisite knowledge required in this paper and the main result of the article.In chapter 2,we characterize the positive Borel measure? on C for which the induced Toeplitz operator T_? is bounded(or compact)between one doubling Fock space F~p(?)(0<<?)and another~?(?)in terms of averaging functions and t-Berezin transform.In chapter 3,We use an unitray operator U_z to obtain sufficient conditions for boundedness of these operators.Also,an example is given to show that the condition is not necessary,and two conditions for compactness of these opertors are given.