Weak-type maximal function estimates on the infinite-dimensional torus
We prove necessary and sufficient conditions for the weak- $L^p$ boundedness, for $p\in (1,\infty)$, of a maximal operator on the infinite-dimensional torus. In the endpoint case $p=1$ we obtain the same weak-type inequality enjoyed by the strong maximal function in dimension two. Our results are qu...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1717 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/1717 |
| Access Level: | acceso abierto |
| Palabra clave: | Infinite-dimensional torus Maximal operator Weak-type estimate |
| Sumario: | We prove necessary and sufficient conditions for the weak- $L^p$ boundedness, for $p\in (1,\infty)$, of a maximal operator on the infinite-dimensional torus. In the endpoint case $p=1$ we obtain the same weak-type inequality enjoyed by the strong maximal function in dimension two. Our results are quantitatively sharp. |
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