Maximal operators of commutators of Bochner-Riesz means with Lipschitz functions

Abstract

This paper presents a weighted L2 estimate with power weights for the maximal operator of commutators generated by compactly supported multipliers and Lipschitz functions. As an application, we study the almost convergence of the commutators, which is generated by the Bochner-Riesz means under the critical index and Lipschitz functions, for functions in Lp (p ⩾ 2).