An endpoint estimate for the maximal Calder\'on commutator with rough kernel
| Autor: | Hu, Guoen, Lai, Xudong, Tao, Xiangxing, Xue, Qingying |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, the authors consider the endpoint estimates for the maximal Calder\'on commutator defined by $$T_{\Omega,\,a}^*f(x)=\sup_{\epsilon>0}\Big|\int_{|x-y|>\epsilon}\frac{\Omega(x-y)}{|x-y|^{d+1}} \big(a(x)-a(y)\big)f(y)dy\Big|,$$ where $\Omega$ is homogeneous of degree zero, integrable on $S^{d-1}$ and has vanishing moment of order one, $a$ be a function on $\mathbb{R}^d$ such that $\nabla a\in L^{\infty}(\mathbb{R}^d)$. The authors prove that if $\Omega\in L\log L(S^{d-1})$, then $T^*_{\Omega,\,a}$ satisfies an endpoint estimate of $L\log\log L$ type. Comment: 25 pages |
| Databáze: | arXiv |
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