The Boundedness Of The Maximal Bochner-Riesz Communtator Operator On Several Spaces

In this paper, we mainly discuss the Boundness of the maximal Bochner-Riesz communtationoperator on several spaces.Chapter 1, introdouces the backgrounds of operators and the techniques of this paper.In chapter 2, we study the endpnint boundedness of maximal commutator Bochner-Rieszoperator on several Morrey spaces; This section has been published in5Analysis in Theory andApplications6, in volume 26 (1) and employed by zhejiang university journal.In chapter 3, we obtain the boundedness of maximal Bochner-Riesz operator and maximalcommutator on Morrey type spaces: When 1≤p <∞, 0 <λ< 1, then B_δ~b,?(f) is bounded onL~p,λ(R_n) space; If 1≤p <∞, then B_δ~b,(f) is bounded on the space of Lp,φ(R_n). This section hasbeen published in Jiangxi normal university journals (natural sciences), in volume 34 (4).In chapter 4, we establish the boundness for maximal commutators of the Bochner-Rieszoperator from local Hardy space to h1q(R_n) space. This section has been published in Mathematicalannual in volume 32 (3).