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arXiv · 2605.25919

Sparse domination of Calder\'on-Zygmund operators by mean oscillations

Andrei K. Lerner
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Abstract

We show that if $T$ is a Dini-continuous Calder\'on--Zygmund operator satisfying $T(1)=0$, then the usual sparse domination for $T$ can be sharpened by replacing local averages with local mean oscillations. This extends a result of Benea and Bernicot for smoother kernels to the more general Dini-continuous setting. As an application, we characterize the Calder\'on--Zygmund operators for which a pointwise Sobolev-type inequality holds: this is the case if and only if $T(1)\in L^\infty$. This answers a recent question of Hoang, Moen and P\'erez.

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Andrei K. Lerner. 2026-05-25. Sparse domination of Calder\'on-Zygmund operators by mean oscillations. https://arxiv.org/abs/2605.25919

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