Abstract:In this note, we show that if $T$ is a Calderón--Zygmund operator satisfying $T(1)=0$, then the usual sparse domination for $T$ can be sharpened by replacing local averages by local mean oscillations. As an application, we characterize the Calderón--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 Pérez.
| Comments: | 9 pages |
| Subjects: | Classical Analysis and ODEs (math.CA); Functional Analysis (math.FA) |
| Cite as: | arXiv:2605.25919 [math.CA] |
| (or arXiv:2605.25919v1 [math.CA] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25919 arXiv-issued DOI via DataCite (pending registration) |
From: Andrei Lerner [view email]
[v1]
Mon, 25 May 2026 14:56:32 UTC (8 KB)
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