A Direct Proof of Hardy-Littlewood Maximal Inequality for Operator-valued Functions

TL;DR

This paper provides a direct proof of the Hardy-Littlewood maximal inequality specifically for operator-valued functions within the range 2<p<∞, advancing the theoretical understanding of maximal inequalities in operator theory.

Contribution

It introduces a new direct proof method for the operator-valued Hardy-Littlewood maximal inequality, which was previously established through different approaches.

Findings

Established the inequality for 2<p<∞

Provided a new direct proof technique

Enhanced understanding of operator-valued maximal functions

Abstract

We give a direct proof of the operator valued Hardy-Littlewood maximal inequality for $2<p<\infty$.