A compact extension of Journé's $T1$ theorem on product spaces
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914891617533952 |
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| author | Cao, Mingming Yabuta, Kôzô Yang, Dachun |
| author_facet | Cao, Mingming Yabuta, Kôzô Yang, Dachun |
| contents | We prove a compact version of the $T1$ theorem for bi-parameter singular integrals. That is, if a bi-parameter singular integral operator $T$ admits the compact full and partial kernel representations, and satisfies the weak compactness property, the diagonal $\mathrm{CMO}$ condition, and the product $\mathrm{CMO}$ condition, then $T$ can be extended to a compact operator on $L^p(w)$ for all $1<p<\infty$ and $w \in A_p(\mathbb{R}^{n_1} \times \mathbb{R}^{n_2})$. Even in the unweighted setting, it is the first time to give a compact extension of Journé's $T1$ theorem on product spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_10965 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A compact extension of Journé's $T1$ theorem on product spaces Cao, Mingming Yabuta, Kôzô Yang, Dachun Classical Analysis and ODEs Functional Analysis 42B20, 42B25, 42B35 We prove a compact version of the $T1$ theorem for bi-parameter singular integrals. That is, if a bi-parameter singular integral operator $T$ admits the compact full and partial kernel representations, and satisfies the weak compactness property, the diagonal $\mathrm{CMO}$ condition, and the product $\mathrm{CMO}$ condition, then $T$ can be extended to a compact operator on $L^p(w)$ for all $1<p<\infty$ and $w \in A_p(\mathbb{R}^{n_1} \times \mathbb{R}^{n_2})$. Even in the unweighted setting, it is the first time to give a compact extension of Journé's $T1$ theorem on product spaces. |
| title | A compact extension of Journé's $T1$ theorem on product spaces |
| topic | Classical Analysis and ODEs Functional Analysis 42B20, 42B25, 42B35 |
| url | https://arxiv.org/abs/2303.10965 |