Kyoto Journal of Mathematics

Mapping properties of the discrete fractional maximal operator in metric measure spaces

Toni Heikkinen, Juha Kinnunen, Juho Nuutinen, and Heli Tuominen

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This work studies boundedness properties of the fractional maximal operator on metric measure spaces under standard assumptions on the measure. The main motivation is to show that the fractional maximal operator has similar smoothing and mapping properties as the Riesz potential. Instead of the usual fractional maximal operator, we also consider a so-called discrete maximal operator which has better regularity. We study the boundedness of the discrete fractional maximal operator in Sobolev, Hölder, Morrey, and Campanato spaces. We also prove a version of the Coifman– Rochberg lemma for the fractional maximal function.

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Kyoto J. Math., Volume 53, Number 3 (2013), 693-712.

First available in Project Euclid: 19 August 2013

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Primary: 42B25: Maximal functions, Littlewood-Paley theory 35J60: Nonlinear elliptic equations 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems


Heikkinen, Toni; Kinnunen, Juha; Nuutinen, Juho; Tuominen, Heli. Mapping properties of the discrete fractional maximal operator in metric measure spaces. Kyoto J. Math. 53 (2013), no. 3, 693--712. doi:10.1215/21562261-2265932.

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