Compactness of commutators of rough singular integrals

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 Calderón-Zygmund operators. Additionally, we prove a matrix-weighted compactness result for $[b,T_{\Omega }]$ by applying the so-called matrix-weighted Kolmogorov-Riesz theorem.

arXiv comment22 pages; added acknowledgements and a remark and corrected typos