The Properties Of Several Kinds Of Operators On Fock-type Spaces

In this thesis,we have studied the operators of the boundedness and compactness on Fock-type spaces,using the equivalent descriptions of norm and the number of re-lated estimates,got the operators of the boundedness and compactness of equivalent characterizations on the Fock-type spaces.This thesis is divided into four chapters.The first chapter gives some basic definitions and related knowledge about Fock-type space,and introduces the research status and research significance of Fock-type space and the operators in Fock space at home and abroad..The second chapter discusses the Fock space F?2 to Fock-Sobolev space F?2,m on the properties of weighted composition operators,using an important estimate,ob-tained the boundedness and compactness of several equivalent characterizations,and gives a necessary and sufficient condition of the operator is Hilbert-Schmidt operator on the F?2,m.The third chapter studies two classes Volterra integral operators the boundedness and compactness of the Fock-Sobolev spaces,use norm topy various characterizations and properties of Bergman kernel function is related to estimate,obtained about the some equivalent characterizations of the boundedness and compactness.The fourth chapter studies the Fock-Sobolev space of two classes of generalized composition operators of the boundedness and compactness,using norm equivalent de-scriptions,Bergman kernel function estimation,and use several estimation functions,obtained about the some equivalent characterizations of the boundedness and compact-ness.