The Study Of (Weighted) Composition Operators And Integral-type Composition Operators On Some Spaces Of Analytic Functions

(Weighted)composition operators and integral-type composition operators play important roles on varieties kinds of analytic function spaces,whose main target is to relate the operator theoretic properties to the function theoretic properties.In this paper,we will study some properties of(weighted)composition operators and integral-type composition operators on three kinds of special function spaces.This paper involves five chapters.In the first chapter,we introduce the background and present situation of our study and present the problems to be investigated.In the second chapter,some basic notions and basic concepts of relative analytic function spaces and the operators are presented.In the third chapter,we study the weighted composition operators on Fock-Sobolev spaces in several complex variables.Firstly,we completely characterize the bounded-ness and compactness of weighted composition operators on Fock-Sobolev spaces by using the singular value decomposition of an n×n matrix.And then,we prove that no nontrivial unitary,self-adjoint and-symmetric weighted composition operators exist on Fock-Sobolev spaces.In the fourth chapter,we study the integral-type composition operators on a class of Fock space with rapidly increasing weights.Firstly,we obtain a upper pointwise estimate for the Bergman kernel of this kind of Fock space by using a weighted L~2estimate for the(?)equation.And then we completely characterize the boundedness and compactness of the integral-type composition operators on this kind of Fock space via Carleson measure and Berezin type transform.The last chapter is focus on the composition operators on variable exponent Bergman spaces.Firstly,we obtain the atomic decomposition for variable exponent Bergman s-paces.Secondly,we give some characterization for the boundedness and compactness of composition operators on these spaces via the Carleosn measure.Finally,we inves-tigate the difference and linear combination of two composition operators on variable exponent Bergman spaces.