Two-weight Norm Inequalities For Maximal Operators On Weighted Morrey Spaces

In this paper, by using the method of E. T. Sawyer and C. Pérez on the proofs of the twoweighted norm inequality for Hardy-Littlewood maximal operator on weighted Lebesguespaces and recently the method of estimating the boundedness of operators on weightedMorrey spaces, we study the two weighted norm inequalities for Hardy-Littlewood maximaloperator and Orlicz maximal operators on weighted Morrey spaces. The individual chaptersare scheduled as follows:Chapter1: We introduce the theory of weighted Morrey spaces and the current researchcircumstance on the theory of two weighted norm inequalities of operators. The maintheorems which would be proved afterward are listed in this chapter.Chapter2: By using the method of the testing condition, we’ll prove the two-weightboundedness of Hardy-Littlewood maximal operator on weighted Morrey spaces. Moreover,the two-weight weak (1,1) boundedness of this operator is considered by us in the end of thischapter.Chapter3: By using the method of the Ap-bump condition, we’ll prove the two-weightboundedness of Hardy-Littlewood maximal operator on weighted Morrey spaces.Chapter4: In this chapter, we’ll generalize those results in chapter three to the case ofOrlicz maximal operator.Chapter5: An objective summaries of our researchs have been made in this chapter,thereafter we’ll give a future perspective of the two-weight theory.