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arXiv · 2503.05390

Compactness of commutators of rough singular integrals

Aapo Laukkarinen·Jaakko Sinko
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Abstract

We study the two-weighted off-diagonal compactness of commutators of rough singular integral operators $T_\Omega$ that are associated with a kernel $\Omega\in L^q(\mathbb{S}^{d-1})$. We establish a characterisation of compactness of the commutator $[b,T_\Omega]$ in terms of the function $b$ belonging to a suitable space of functions with vanishing mean oscillation. Our results expand upon the previous compactness characterisations for Calder\'on-Zygmund operators. Additionally, we prove a matrix-weighted compactness result for $[b,T_\Omega]$ by applying the so-called matrix-weighted Kolmogorov-Riesz theorem.

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Aapo Laukkarinen, Jaakko Sinko. 2025-03-07. Compactness of commutators of rough singular integrals. https://arxiv.org/abs/2503.05390

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