The Weighted Estimates For The Maximal Bochner-riesz Operator And Its Commutator

In this paper, we study the weighted estimates for the maximal Bochner-Riesz commutatorson several spaces. This paper is constituted with five chapters.In chapter1, we introduce the background and main results about Bochner-Riesz operatorand its commutators.In chapter2, we establish the poistwise estimates for the sharp maximal function of maximalBochner-Riesz commutators generalized by Bδtand a weighted Lipschitz function b.In chapter3, we introduce the Boundness estimates of maximal commutators for Bochner-Riesz operator generalized by Bocher-Riesz operator Bδtand weighted function b on the weightedMorrey space.In chapter4, we discuss the two weighted estimates of maximal commutators for Bochner-Riesz operator on the BMO space.In chapter5, we establish the boundness of the maximal Bochner-Riesz commutators gener-alized by Bδtand a λ-center BMO function b on the Morrey space.