An Integral Estimate And Composition Operator On F(p,q,s) Space

In this dissertation,Firstly,We discussed the problem of a typical integral estimate on the unit ball of Cn.The bidirectional estimates of all 11 cases are given.Secondly,We discussed the problem of composition operator on F(p,q,s)tytpe spaces.The sufficient conditions and necessary conditions that composition operators is bounded or compact on A(p,q,s)type spaces are given.At the same time,The sufficient conditions and necessary conditions that composition operators is bounded or compact on F(p,q,s)type spaces are given also.Especially,The simple sufficient and necessary conditions of compactness on F(p,q,s)are given.This dissertation consists of three chapters.In the first chapter,we give a comprehensive summary about the research background and the conclusions that we obtain.In the second chapter,we give bidirectional estimates of a.ll 11 cases for a bi-variables typical integral on the unit ball,That is theorem 2.3.1.In the third chapter,First,We give the bounded and compa.ct conditions of composition operator on A(p,q,s)type spaces in the unit ball of Cn,that is theorem 3.3.1 and theorem 3.3.2.Next we give the bounded and compact conditions of composition operators on F(p,q,s)type spaces in the unit ball of Cn,that is t,heorem 3.3.3 and theorem 3.3.4.Finally,The simple sufficient and necessary conditions of compactness on F(p,q,s)are given,that is theorem 3.3.5.