Publicação
Self-improving boundedness of the maximal operator on quasi-Banach lattices over spaces of homogeneous type
| Resumo: | We prove the self-improvement property of the Hardy–Littlewood maximal operator on quasi-Banach lattices with the Fatou property in the setting of spaces of homogeneous type. Our result is a generalization of the boundedness criterion obtained in 2010 by Lerner and Ombrosi for maximal operators on quasi-Banach function spaces over Euclidean spaces. The specialty of the proof for spaces of homogeneous type lies in using adjacent grids of Hytönen–Kairema dyadic cubes and studying the maximal operator alongside its “dyadic” version. Then we apply the obtained result to variable Lebesgue spaces over spaces of homogeneous type. |
|---|---|
| Autores principais: | Shalukhina, Alina |
| Assunto: | Hardy–Littlewood maximal operator Quasi-Banach lattice Self-improving property Space of homogeneous type Variable Lebesgue space “Dyadic” maximal operator Analysis Applied Mathematics |
| Ano: | 2025 |
| 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: | We prove the self-improvement property of the Hardy–Littlewood maximal operator on quasi-Banach lattices with the Fatou property in the setting of spaces of homogeneous type. Our result is a generalization of the boundedness criterion obtained in 2010 by Lerner and Ombrosi for maximal operators on quasi-Banach function spaces over Euclidean spaces. The specialty of the proof for spaces of homogeneous type lies in using adjacent grids of Hytönen–Kairema dyadic cubes and studying the maximal operator alongside its “dyadic” version. Then we apply the obtained result to variable Lebesgue spaces over spaces of homogeneous type. |
|---|