Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Laukkarinen, Aapo, Sinko, Jaakko
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979344282
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