Weak type bounds for rough maximal singular integrals near $L^1$
| Autor: | Ankit Bhojak, Parasar Mohanty |
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| Rok vydání: | 2021 |
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| DOI: | 10.48550/arxiv.2110.00832 |
| Popis: | In this paper it is shown that for $\Omega\in L\log L(\mathbb{S}^{d-1})$, the rough maximal singular integral operator $T_\Omega^*$ is of weak type $L\log\log L(\mathbb{R}^d)$. Furthermore, for $w\in A_1$ and $\Omega\in L^\infty(\mathbb{S}^{d-1})$, it is shown that $T_\Omega^*$ is of weak type $L\log\log L(w)$ with weight dependence $[w]_{A_1}[w]_{A_{\infty}}\log([w]_{A_{\infty}}+1),$ which is same as the best known constant for the singular integral $T_\Omega$. Comment: 23 pages. Comments are welcome |
| Databáze: | OpenAIRE |
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