Riesz-Schur transforms
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866912128412155904 |
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| author | González-Pérez, Adrian Parcet, Javier García, Jorge Pérez Ricard, Éric |
| author_facet | González-Pérez, Adrian Parcet, Javier García, Jorge Pérez Ricard, Éric |
| contents | We investigate nontrigonometric forms of Riesz transforms in the context of Schur multipliers. This refines Grothendieck-Haagerup's endpoint criterion with a new condition for the Schatten p-boundedness of Schur multipliers and strengthens Potapov/Sukochev's solution of Arazy's conjecture. We recover as well dimension-free estimates for trigonometric Riesz transforms. Our discrete approach is much simpler than previous harmonic analysis and probabilistic approaches. As an application, we find a very simple proof of recent criteria for Schur multipliers of Hörmander-Mikhlin and Marcinkiewicz type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09324 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Riesz-Schur transforms González-Pérez, Adrian Parcet, Javier García, Jorge Pérez Ricard, Éric Functional Analysis Operator Algebras We investigate nontrigonometric forms of Riesz transforms in the context of Schur multipliers. This refines Grothendieck-Haagerup's endpoint criterion with a new condition for the Schatten p-boundedness of Schur multipliers and strengthens Potapov/Sukochev's solution of Arazy's conjecture. We recover as well dimension-free estimates for trigonometric Riesz transforms. Our discrete approach is much simpler than previous harmonic analysis and probabilistic approaches. As an application, we find a very simple proof of recent criteria for Schur multipliers of Hörmander-Mikhlin and Marcinkiewicz type. |
| title | Riesz-Schur transforms |
| topic | Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2411.09324 |