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April 2015 Regularity of the local fractional maximal function
Toni Heikkinen, Juha Kinnunen, Janne Korvenpää, Heli Tuominen
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Ark. Mat. 53(1): 127-154 (April 2015). DOI: 10.1007/s11512-014-0199-2


This paper studies smoothing properties of the local fractional maximal operator, which is defined in a proper subdomain of the Euclidean space. We prove new pointwise estimates for the weak gradient of the maximal function, which imply norm estimates in Sobolev spaces. An unexpected feature is that these estimates contain extra terms involving spherical and fractional maximal functions. Moreover, we construct several explicit examples, which show that our results are essentially optimal. Extensions to metric measure spaces are also discussed.

Funding Statement

This work was supported by the Academy of Finland.


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Toni Heikkinen. Juha Kinnunen. Janne Korvenpää. Heli Tuominen. "Regularity of the local fractional maximal function." Ark. Mat. 53 (1) 127 - 154, April 2015.


Received: 16 October 2013; Published: April 2015
First available in Project Euclid: 30 January 2017

zbMATH: 1316.42019
MathSciNet: MR3319617
Digital Object Identifier: 10.1007/s11512-014-0199-2

Rights: 2014 © Institut Mittag-Leffler


Vol.53 • No. 1 • April 2015
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