Publicacions Matemàtiques

Smoothing properties of the discrete fractional maximal operator on Besov and Triebel-Lizorkin spaces

Toni Heikkinen and Heli Tuominen

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Abstract

Motivated by the results of Korry, and Kinnunen and Saksman, we study the behaviour of the discrete fractional maximal operator on fractional Hajłasz spaces, Hajłasz-Besov, and Hajłasz-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.

Article information

Source
Publ. Mat., Volume 58, Number 2 (2014), 379-399.

Dates
First available in Project Euclid: 21 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.pm/1405949324

Mathematical Reviews number (MathSciNet)
MR3264503

Zentralblatt MATH identifier
1304.62118

Subjects
Primary: 42B25: Maximal functions, Littlewood-Paley theory 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems

Keywords
Besov space fractional maximal function fractional Sobolev space Triebel-Lizorkin space metric measure space

Citation

Heikkinen, Toni; Tuominen, Heli. Smoothing properties of the discrete fractional maximal operator on Besov and Triebel-Lizorkin spaces. Publ. Mat. 58 (2014), no. 2, 379--399. https://projecteuclid.org/euclid.pm/1405949324


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