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Noncommutative maximal operators with rough kernels

Xudong Lai

Vol. 17 (2024), No. 4, 1439–1471
Abstract

This paper is devoted to the study of noncommutative maximal operators with rough kernels. More precisely, we prove the weak-type (1,1) boundedness for noncommutative maximal operators with rough kernels. The proof of the weak-type (1,1) estimate is based on the noncommutative Calderón–Zygmund decomposition. To deal with the rough kernel, we use the microlocal decomposition in the proofs of both the bad and good functions.

Keywords
noncommutative $L_p$ space, weak (1,1) bound, maximal operator, singular integral operator, rough kernel
Mathematical Subject Classification
Primary: 46L52, 42B25
Secondary: 46L51, 42B20
Milestones
Received: 8 March 2022
Revised: 9 July 2022
Accepted: 30 August 2022
Published: 17 May 2024
Authors
Xudong Lai
Institute for Advanced Study in Mathematics
Harbin Institute of Technology
Harbin
China

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