Compactness of commutators of rough singular integrals
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910874903511040 |
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| author | Laukkarinen, Aapo Sinko, Jaakko |
| author_facet | Laukkarinen, Aapo Sinko, Jaakko |
| contents | We study the two-weighted off-diagonal compactness of commutators of rough singular integral operators $T_Ω$ that are associated with a kernel $Ω\in L^q(\mathbb{S}^{d-1})$. We establish a characterisation of compactness of the commutator $[b,T_Ω]$ 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 $[b,T_Ω]$ by applying the so-called matrix-weighted Kolmogorov-Riesz theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05390 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Compactness of commutators of rough singular integrals Laukkarinen, Aapo Sinko, Jaakko Classical Analysis and ODEs Functional Analysis 42B20 (Primary) 47B47 (Secondary) We study the two-weighted off-diagonal compactness of commutators of rough singular integral operators $T_Ω$ that are associated with a kernel $Ω\in L^q(\mathbb{S}^{d-1})$. We establish a characterisation of compactness of the commutator $[b,T_Ω]$ 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 $[b,T_Ω]$ by applying the so-called matrix-weighted Kolmogorov-Riesz theorem. |
| title | Compactness of commutators of rough singular integrals |
| topic | Classical Analysis and ODEs Functional Analysis 42B20 (Primary) 47B47 (Secondary) |
| url | https://arxiv.org/abs/2503.05390 |