Noncommutative maximal operators with rough kernels

preprint2022arXivOpen access

Abstract

This paper is devoted to the study of noncommutative maximal operators with rough kernels. More precisely, we prove the weak type (1,1)(1,1) boundedness for noncommutative maximal operators with rough kernels. The proof of 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.

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