## Kyoto Journal of Mathematics

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

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 19 August 2013

https://projecteuclid.org/euclid.kjm/1376917630

Digital Object Identifier
doi:10.1215/21562261-2265932

Mathematical Reviews number (MathSciNet)
MR3102566

Zentralblatt MATH identifier
1280.42012

#### Citation

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. https://projecteuclid.org/euclid.kjm/1376917630

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