Calderón-Zygmund theory with noncommuting kernels via $H_1^c$
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910015742279680 |
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| author | Cano-Mármol, Antonio Ismael Ricard, Éric |
| author_facet | Cano-Mármol, Antonio Ismael Ricard, Éric |
| contents | We study an alternative definition of the $H_1$-space associated to a semicommutative von Neumann algebra $L_\infty(\mathbb{R}) \overline{\otimes} \mathcal{M}$, first studied by Mei. We identify a "new" description for atoms in $H_1$. We then explain how they can be used to study $H_1^c$-$L_1$ endpoint estimates for Calderón-Zygmund operators with noncommuting kernels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_01266 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Calderón-Zygmund theory with noncommuting kernels via $H_1^c$ Cano-Mármol, Antonio Ismael Ricard, Éric Functional Analysis Operator Algebras 42B20, 42B35, 46L51, 46L52 We study an alternative definition of the $H_1$-space associated to a semicommutative von Neumann algebra $L_\infty(\mathbb{R}) \overline{\otimes} \mathcal{M}$, first studied by Mei. We identify a "new" description for atoms in $H_1$. We then explain how they can be used to study $H_1^c$-$L_1$ endpoint estimates for Calderón-Zygmund operators with noncommuting kernels. |
| title | Calderón-Zygmund theory with noncommuting kernels via $H_1^c$ |
| topic | Functional Analysis Operator Algebras 42B20, 42B35, 46L51, 46L52 |
| url | https://arxiv.org/abs/2309.01266 |