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...

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Detalles Bibliográficos
Autores: Kosz, D., Rey, G., Roncal, L.
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
Descripción
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.