Some Operators On Holomorphic Fock Spaces

This dissertation deals with holomorphic Fock spaces on Cn,our works are mainly about the characterizations of Hankel operators,small Hankel operators and Toeplitz operators.In order to do that,we introduce a class of(s,p)-integrable mean oscillation spaces IMO and a kind of generalized convolution operators Tf,(?)We focus on the decomposition for IMO spaces and boundedness of the generalized convolution operators acting between LP spaces with different exponents.By using these tools we can obtain the important characteristics of these operators.This thesis consists of six chapters.In the first chapter,we introduce the background,notations and definitions,which will be used throughout this thesis.And also,we list the main results of our dissertation.Chapter 2 is aimed at investigating Hankel operators induced by real-valued functions f acting from F?p to L?q.As a corollary,for all possible 1?p,q<?,we characterize the boundedness and compactness of Hankel operators induced by antiholomorphic functions acting from F?pto L?q.To this end.we first introduce a class of of(s,p)-integrable mean oscillation spaces IMO,which is a generalization of BMO spaces.We study some basic properties of IMO spaces.In addition,we discuss the boundedness of the generalized convolution operators Tf,(?)acting between LP spaces with different exponents.In chapter 3,for all possible 1?p,q<?,we characterize the boundedness and compactness of small Hankel operators induced by some functions from F?ptoF?q,As an application,we characterize the boundedness of Hankel forms on F?p×F?q,Furthermore,we obtain the weak factorization for Fock spaces.Chapter 5 is devoted to investigate the boundedness and compactness of Toeplitz operators induced by IMO functions for 0<q<p<?.The result is correspond to the case of Toeplitz operators induced by BMO functions for 0<p?q<?In Chapter 5,suppose ? is subharmonic,real-valued and not,identically zero on C with v = ??dA,we study the Schatten p class of Hankel operators acting on weighted Fock spaces F?2 whenever 1<p<2.This result together with the similar one for 2 ?p<? characterize the Schatten p class of Hankel operators acting on weighted Fock spaces F?2 for all 1 ?p<?.Finally,we summarize our main results briefly and list some points for future study.