Compact Composition Operators on Weighted Hardy and Bergman Spaces

Over the last ten years, the theory of Hardy and Bergman Spaces has undergone a remarkable metamorphosis. The research originated from a study of weighted Hardy and Bergman Spaces that revolve around the composition operators and inequalities is to present the latest development, mostly achieved in the thesis form. In particular, gradute students and new researchers in the field will have access to the theory from an almost self contained and readable source. We study the action of composition operators on Sobolev Spaces of analytic functions in some weighted Bergman and Hardy Spaces on the unit disc. composition operators mapping into the Hardy Space are included by making particular choices for the weights. In the thesis we will explain some of the important results of compact composition operators on weighted Hardy and Bergman Spaces.

Autorentext

Elhadi Elnour Elniel Dalam, was born in Sudan,( Honors B.Sc. in Mathematics-College of Sciences 1996,M.Sc in Mathematics-College of Graduate studies 2000, Ph.D.in Mathematics(Functional Analysis)College of Graduate studies 2007)Sudan University of Science and Technology,Assistant professor at Taif University Saudi Arabia and I have many Publishes