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...

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Detalles Bibliográficos
Autores: Heikkinen, Toni, Tuominen, Heli
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:119033
Acceso en línea:https://ddd.uab.cat/record/119033
https://dx.doi.org/urn:doi:10.5565/PUBLMAT_58214_19
Access Level:acceso abierto
Palabra clave:Besov space
Fractional maximal function
Fractional Sobolev space
Triebel-Lizorkin space
Metric measure space
Descripción
Sumario: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.