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arXiv · 2501.04951

Weighted norm estimates of noncommutative Calder\'{o}n-Zygmund operators

Wenfei Fan·Yong Jiao·Lian Wu·Dejian Zhou
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Abstract

This paper is devoted to studying weighted endpoint estimates of operator-valued singular integrals. Our main results include weighted weak-type $(1,1)$ estimate of noncommutative maximal Calder\'{o}n-Zygmund operators, corresponding version of square functions and a weighted $H_1- L_1$ type inequality. All these results are obtained under the condition that the weight belonging to the Muchenhoupt $A_1$ class and certain regularity assumptions imposed on kernels which are weaker than the Lipschitz condition.

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Wenfei Fan, Yong Jiao, Lian Wu, Dejian Zhou. 2025-01-09. Weighted norm estimates of noncommutative Calder\'{o}n-Zygmund operators. https://arxiv.org/abs/2501.04951

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