Endpoint weak-type bounds beyond Calderón-Zygmund theory
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914948765974528 |
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| author | Nieraeth, Zoe Stockdale, Cody B. |
| author_facet | Nieraeth, Zoe Stockdale, Cody B. |
| contents | We prove weighted weak-type $(r,r)$ estimates for operators satisfying $(r,s)$ limited-range sparse domination of $\ell^q$-type. Our results contain improvements for operators satisfying limited-range and square function sparse domination. In the case of operators $T$ satisfying standard sparse form domination such as Calderón-Zygmund operators, we provide a new and simple proof of the sharp bound $$
\|T\|_{L^1_w(\mathbf{R}^d)\rightarrow L^{1,\infty}_w(\mathbf{R}^d)} \lesssim [w]_1(1+\log [w]_{\text{FW}}). $$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08921 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Endpoint weak-type bounds beyond Calderón-Zygmund theory Nieraeth, Zoe Stockdale, Cody B. Classical Analysis and ODEs Functional Analysis 42B20, 42B25 We prove weighted weak-type $(r,r)$ estimates for operators satisfying $(r,s)$ limited-range sparse domination of $\ell^q$-type. Our results contain improvements for operators satisfying limited-range and square function sparse domination. In the case of operators $T$ satisfying standard sparse form domination such as Calderón-Zygmund operators, we provide a new and simple proof of the sharp bound $$ \|T\|_{L^1_w(\mathbf{R}^d)\rightarrow L^{1,\infty}_w(\mathbf{R}^d)} \lesssim [w]_1(1+\log [w]_{\text{FW}}). $$ |
| title | Endpoint weak-type bounds beyond Calderón-Zygmund theory |
| topic | Classical Analysis and ODEs Functional Analysis 42B20, 42B25 |
| url | https://arxiv.org/abs/2409.08921 |