Sharp $B$-Maximal Function Estimates and Boundedness for Some Integral Operators to the Inequalities

Abstract

In this paper, we first establish the relation between $B$-maximal and sharp $B$-maximal functions generated by the generalized translation operator connected with the Laplace-Bessel differential operator. We then prove some sharp $B$-maximal function estimates and present an application using these sharp estimates to study singular integral operators. We finally obtain the boundedness of the Littlewood-Paley $g$-function related to the Laplace-Bessel differential operator on generalized $B$-Morrey spaces.