Boundedness Of The Hausdorff Operators On The Power Weighted Hardy Spaces

In this paper,we study the boundedness of Hausdorff operators on the weighted Hardy spaces and obtain some sufficient conditions for the boundedness of Hausdorff operators on the weighted Hardy spaces.Our result improves some known results and it is sharp in the size condition.The paper is divided into three chapters.In the first chapter we mainly introduce the developments of the Hausdorff operators and the main result of the paper.In the second chapter we give the definitions and some properties of the Ap weights,the definitions of weighted Hardy spaces and some lemmas that will be used in this thesis.In the third chapter the proof of the main theorem is given.The main techniques here are the atomic decomposition of weighted Hardy spaces and the Riesz transforms.