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arXiv · 2501.06567

Two inequalities for commutators of singular integral operators satisfying H\"{o}rmander conditions of Young type

Yuru Li·Jiawei Tan·Qingying Xue
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Abstract

In this paper, we systematically study the Fefferman-Stein inequality and Coifman-Fefferman inequality for the general commutators of singular integral operators that satisfy H\"{o}rmander conditions of Young type. Specifically, we first establish the pointwise sparse domination for these operators. Then, relying on the dyadic analysis, the Fefferman-Stein inequality with respect to arbitrary weights and the quantitative weighted Coifman-Fefferman inequality are demonstrated. We decouple the relationship between the number of commutators and the index $\varepsilon$, which essentially improved the results of P\'{e}rez and Rivera-R\'{\i}os (Israel J. Math., 2017). As applications, it is shown that all the aforementioned results can be applied to a wide range of operators, such as singular integral operators satisfying the $L^r$-H\"{o}rmander operators, $\omega$-Calder\'{o}n-Zygmund operators with $\omega$ satisfying a Dini condition, Calder\'{o}n commutators, homogeneous singular integral operators and Fourier multipliers.

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Yuru Li, Jiawei Tan, Qingying Xue. 2025-01-11. Two inequalities for commutators of singular integral operators satisfying H\"{o}rmander conditions of Young type. https://arxiv.org/abs/2501.06567

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