Arkiv för Matematik

  • Ark. Mat.
  • Volume 53, Number 1 (2015), 127-154.

Regularity of the local fractional maximal function

Toni Heikkinen, Juha Kinnunen, Janne Korvenpää, and Heli Tuominen

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Abstract

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.

Note

This work was supported by the Academy of Finland.

Article information

Source
Ark. Mat., Volume 53, Number 1 (2015), 127-154.

Dates
Received: 16 October 2013
First available in Project Euclid: 30 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485802702

Digital Object Identifier
doi:10.1007/s11512-014-0199-2

Mathematical Reviews number (MathSciNet)
MR3319617

Zentralblatt MATH identifier
1316.42019

Rights
2014 © Institut Mittag-Leffler

Citation

Heikkinen, Toni; Kinnunen, Juha; Korvenpää, Janne; Tuominen, Heli. Regularity of the local fractional maximal function. Ark. Mat. 53 (2015), no. 1, 127--154. doi:10.1007/s11512-014-0199-2. https://projecteuclid.org/euclid.afm/1485802702


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