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arXiv · 2009.11650

An endpoint estimate for the commutators of singular integral operators with rough kernels

Guoen Hu·Xiangxing Tao
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Abstract

Let $\Omega$ be homogeneous of degree zero and have mean value zero on the unit sphere ${S}^{d-1}$, $T_{\Omega}$ be the homogeneous singular integral operator with kernel $\frac{\Omega(x)}{|x|^d}$ and $T_{\Omega,\,b}$ be the commutator of $T_{\Omega}$ with symbol $b$. In this paper, we prove that if $\Omega\in L(\log L)^2(S^{d-1})$, then for $b\in {\rm BMO}(\mathbb{R}^d)$, $T_{\Omega,\,b}$ satisfies an endpoint estimate of $L\log L$ type.

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Guoen Hu, Xiangxing Tao. 2020-09-24. An endpoint estimate for the commutators of singular integral operators with rough kernels. https://arxiv.org/abs/2009.11650

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