Regular Mixed Norm Spaces And Its Projection Operator

In this paper,we study the dual spaces and the boundness of the projection operator of regular mixed norm spaces in two types of regions.Firstly,by using the basic properties of regular weights and integral estimates of reproducing kernel functions,the boundedness of projection operators on regular mixed norm spaces of unit disc are obtained,and the results of the boundedness of projection operators have been used to characterize the dual spaces of regular mixed norm space of unit disc.Secondly,the boundedness of the projection operator is proved by the integral estimation of the reproducing kernel on annulus,the result of the boundedness of projection operator on regular mixed norm space of annulus have been used to characterize the dual space of regular mixed norm space on annulus.In Chapter 1,we introduce the research background and present situation of mixed norm spaces.Then we give the preliminary knowledges about regular mixed norm spaces on the unit disk and on the annulus,as well as the main results of this paper.In Chapter 2,we obtained the boundedness of projection operators on regular mixed norm spaces of unit disk,and use results of the boundedness of projection operators to characterize the dual spaces of regular mixed norm spaces on unit disc.In Chapter 3,we obtained the boundedness of projection operators on regular mixed norm spaces of annulus,and use results of the boundedness of projection operators to characterize the dual spaces of regular mixed norm spaces on annulus.