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Smoothing properties of the discrete fractional maximal operator on Besov and Triebel-Lizorkin spaces
Heikkinen, Toni (Aalto University. Department of Mathematics (Aalto, Finlàndia))
Tuominen, Heli (University of Jyväskylä. Department of Mathematics and Statistics)

Data: 2014
Resum: 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.
Drets: Tots els drets reservats
Llengua: Anglès
Document: article ; recerca ; publishedVersion
Matèria: Besov space ; Fractional maximal function ; Fractional Sobolev space ; Triebel-Lizorkin space ; Metric measure space
Publicat a: Publicacions matemàtiques, Vol. 58, Núm. 2 (2014) , p. 379-399, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_58214_19

21 p, 360.3 KB

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