Composition Operators Between P-Bloch Space And Q-Bloch Space In The First Classical Bounded Symmetric Domain

Theory of analytic functions of several variables have been researched late, but therapid development. Although it has a classic functions of one complex variable’s origin,because of its peculiar difficulties and complexity, in a study of key and methods, allthese have significant differences with theory of analytic functions of one complex vari-able(see Complex-Variable Function Theory), and it has become an important branch ofmathematics. Because the nature of functions of several variables have been restrictedto a great extent by definition the geometry of the area and topological characteristics,therefore, the study of key gone from a local nature of the transfer of integrity to grad-ually. It widely uses differential geometry, algebraic geometry, Lie groups, topology,ordinary differential equations and so on neighboring disciplines concepts and methods,and constantly open up and the way forward, updates and expand the research contentand fields.This paper mainly utilizing the definition of p-Bloch type space, decompose polarcoordinates for elements of the first kind classical domain[30]and an automorphism[6]in R_I(m, n) for discussing boundedness of composition operators; use the equivalencecondition of compact operators[24], that is, C_φ: β~p(R_I(m, n))â†'β~q(R_I(m, n)) iscompact if and only if for any bounded sequence {f_v} of β~p(R_I(m, n)) converges to0uniformly on any compact subset of R_I(m, n), we have||C_φf_v β~q||β~qâ†'0, vâ†'∞,finally by structuring a sequence of test function {f_v}, we discuss the compactness ofcomposition operators C_φ.The paper consists of three chapters:In Chapter1, we introduces the development of theory of analytic functions ofseveral variables, researching background, the main work and its prepare knowledge ofthis paper; In Chapter2, we mainly discuss boundedness of composition operators betweenp-Bloch space and q-Bloch space in the first classical bounded symmetric domain;In Chapter3, we mainly discuss compactness of composition operators betweenp-Bloch space and q-Bloch space in the first classical bounded symmetric domain.