Smoothing properties of the discrete fractional maximal operator on Besov and Triebel-Lizorkin spaces
Motivated by the results of Korry, and Kinnunen and Saksman, we study the behaviour of the discrete fractional maximal operator on fractional Hajlasz spaces, Hajlasz-Besov, and Hajlasz-Triebel-Lizorkin spaces on metric measure spaces. We show that the discrete fractional maximal operator maps these...
| Autores: | , |
|---|---|
| Tipo de documento: | artigo |
| Data de publicação: | 2014 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositório: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglês |
| OAI Identifier: | oai:ddd.uab.cat:119033 |
| Acesso em linha: | https://ddd.uab.cat/record/119033 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_58214_19 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Besov space Fractional maximal function Fractional Sobolev space Triebel-Lizorkin space Metric measure space |
| Resumo: | Motivated by the results of Korry, and Kinnunen and Saksman, we study the behaviour of the discrete fractional maximal operator on fractional Hajlasz spaces, Hajlasz-Besov, and Hajlasz-Triebel-Lizorkin spaces on metric measure spaces. We show that the discrete fractional maximal operator maps these spaces to the spaces of the same type with higher smoothness. Our results extend and unify aforementioned results. We present our results in a general setting, but they are new already in the Euclidean case. |
|---|