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An endpoint estimate for the commutators of singular integral operators with rough kernels (2009.11650v4)
Published 24 Sep 2020 in math.CA
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.