Publicação
Hardy-Littlewood maximal operator on the associate space of a Banach function space
| Resumo: | Let ε(X, d, μ) be a Banach function space over a space of homogeneous type (X, d, μ). We show that if the Hardy-Littlewood maximal operator M is bounded on the space ε(X, d, μ), then its boundedness on the associate space ε'(X, d, μ) is equivalent to a certain condition A∞. This result extends a theorem by Andrei Lerner from the Euclidean setting of ℝn to the setting of spaces of homogeneous type. |
|---|---|
| Autores principais: | Karlovich, Alexei Yu |
| Assunto: | Associate space Banach function space Dyadic cubes Hardy-Littlewood maximal operator Space of homogeneous type Analysis Geometry and Topology |
| Ano: | 2019 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade Nova de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório Institucional da UNL |
| Resumo: | Let ε(X, d, μ) be a Banach function space over a space of homogeneous type (X, d, μ). We show that if the Hardy-Littlewood maximal operator M is bounded on the space ε(X, d, μ), then its boundedness on the associate space ε'(X, d, μ) is equivalent to a certain condition A∞. This result extends a theorem by Andrei Lerner from the Euclidean setting of ℝn to the setting of spaces of homogeneous type. |
|---|