Sparse domination of Calderón--Zygmund operators by mean oscillations
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913162309140480 |
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| author | Lerner, Andrei K. |
| author_facet | Lerner, Andrei K. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25919 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sparse domination of Calderón--Zygmund operators by mean oscillations Lerner, Andrei K. Classical Analysis and ODEs Functional Analysis 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. |
| title | Sparse domination of Calderón--Zygmund operators by mean oscillations |
| topic | Classical Analysis and ODEs Functional Analysis |
| url | https://arxiv.org/abs/2605.25919 |