Fefferman–Stein Inequalities for the Hardy–Littlewood Maximal Function on the Infinite Rooted k-ary Tree
In this paper, weighted endpoint estimates for the Hardy–Littlewood maximal function on the infinite rooted k-ary tree are provided. Motivated by Naor and Tao [ 23], the following Fefferman–Stein estimate w({x∈T:Mf(x)>λ})≤cs1λ∫T|f(x)|M(ws)(x)1sdxs>1 is settled, and moreover, it is shown that i...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2020 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/129310 |
| Acceso en línea: | http://hdl.handle.net/11336/129310 |
| Access Level: | acceso abierto |
| Palabra clave: | WEIGHTS MAXIMAL FEFFERMAN-STEIN TREES https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | In this paper, weighted endpoint estimates for the Hardy–Littlewood maximal function on the infinite rooted k-ary tree are provided. Motivated by Naor and Tao [ 23], the following Fefferman–Stein estimate w({x∈T:Mf(x)>λ})≤cs1λ∫T|f(x)|M(ws)(x)1sdxs>1 is settled, and moreover, it is shown that it is sharp, in the sense that it does not hold in general if s=1. Some examples of nontrivial weights such that the weighted weak type (1,1) estimate holds are provided. A strong Fefferman–Stein-type estimate and as a consequence some vector-valued extensions are obtained. In the appendix, a weighted counterpart of the abstract theorem of Soria and Tradacete [ 38] on infinite trees is established. |
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