Bloch Constant Of Bloch Type Space And Integral Operators On Analytic Morrey Space

This thesis is divided into two parts.In the first part,we study sharp distortion theorems for subclasses of ?-Bloch mappings defined in the unit ball of Cn with critical points.Furthermore,the estimates of Bloch constant with respect to these subclasses are given.The rest of the thesis we study several basic operator problems of analytic Morrey space ALp,?.For example:boundedness of Volterra integral operator,boundedness of superposition operator and weighted composition operators.The individual chapters are scheduled as follows:In Chapter 1,we introduce some definitions and notations.Then the main theorem would be proved afterward are listed in this paper.In Chapter 2,we give a new sharp distortion theorems for subclasses of ?-Bloch mappings defined in the unit ball of Cn with critical points.Bying making use of this distortion theorems,we study the estimate of Bloch constant with respect to ???(M).In a similar method,we obtain the Bloch constant Bloc,?(M)estimate.In Chapter 3,we introduce the Morrey space and current research of analytic Morrey space.We also introduced the background and the current research of integral operators.Then we discuss the boundedness of Volterra integral operator from ALP,? to B?.In Chapter 4,we give the boundedness of superposition operator S? and weighted composition operators I?,?(f??))from ALp,? to Ba.We also introduced the background and the current research of superposition operators.