Some Properties Of Analytic Function Spaces On The Bounded Symmetric Domains

The study of analytic function space contains functional properties and analytical properties.Functional properties are studied the global property of analytic function space,Such as the dual space of analytic function space.Analytical properties are mainly studied the propertties of a single function.Such as Taylor coefficient of the analytic function,the relationship between the original function and the derivative function,and these properties are used in multiplier theory.In the complex plane,the properties of analytic function space on unit disk have been improved.However,there are a few investigations about the bounded symmetric domains of multidimensional space.In this paper,we mainly study the fractional derivative theory and multiplier theory between two different function spaces on bounded symmetric domains,These spaces contain Hardy space,Bergman space and complex sequence space.The paper divided into four chapters:In the first chapter,we briefly introduce the background of the fractional derivative theory and multiplier theory and their recent developments.In the second chapter,we mainly expand the fractional derivative theory from the unit disk to the bounded symmetric domains,which improves the fractional derivative theory.In the third chapter,we expand multiplier theory from Hardy space to Bergman space on the bounded symmetric domains.Furthermore,we use the method of appling multiplier language to describe Taylor coefficient,and expand multiplier theory from Bergman space to Hardy space on the bounded symmetric domains.In the fourth chapter,we summarize the content of the previous chapters,and put forward proposals for the further studies about the fractional derivative theory and multiplier theory.