Noncommutative maximal strong $L_p$ estimates of Calder\'on-Zygmund operators

TL;DR

This paper establishes noncommutative maximal inequalities for truncated Calderón-Zygmund operators on operator-valued Lp spaces, extending previous results and answering an open question in the field.

Contribution

It provides the first comprehensive noncommutative maximal inequalities for non-convolution type Calderón-Zygmund operators on operator-valued Lp spaces.

Findings

Proves noncommutative maximal inequalities for all 1<p<∞

Addresses the open question from previous research

Extends the theory to non-convolution type operators

Abstract

In this paper, we obtain the desired noncommutative maximal inequalities of the truncated Calder\'on-Zygmund operators of non-convolution type acting on operator-valued $L_p$-functions for all $1<p<\infty$, answering a question left open in the previous work \cite{HLX}.