Weighted Composition Operators On The Bloch Spaces Of A Bounded Symmetric Domain

In this paper,We study the bounded and the compact weighted composition oper-ators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded symmetric domains,and get some corallaries.In the first chapter,we introduce the development of function space,several com-plex variables and operator theory.And give the symbols and basic definition of this paper.In the second chapter,we define the Bloch space on a bounded symmetric domain as well as collect useful facts about Bloch functions on such domains.The third chapter is the most impotant in this paper,Let BE be a bounded symmet-ric domain realized as the unit open ball of JB*-triples.We will characterize the bound-ed weighted composition operator from the Bloch space B(BE)to weighted Hardy s-pace H_v?(BE)in terms of Kobayashi distance.We also give a sufficient condition for the compactness,and also give the upper bound of its essential norm.As a corollary,we show that the boundedness and compactness are equivalent for composition operator from B(BE)to H?(BE)and weighted composition operators from B(BE)to H_v?,0(BE)when E is a infinite dimension JB*-triple.