The sharp constant for truncated Hardy-Littlewood maximal inequality

Abstract

This paper focuses on the operator norm of the truncated Hardy-Littlewood maximal operator M b a and the strong truncated Hardy-Littlewood maximal operator M b a , respectively. We first present the L 1 -norm of M b a , and then the L 1 -norm of M b a is given. Our study may have some enlightening significance for the research on sharp constant for the classical Hardy-Littlewood maximal inequality.