Arkiv för Matematik

Volume 56 (2018)

Number 1

The variation of the maximal function of a radial function

Pages: 147 – 161

DOI: https://dx.doi.org/10.4310/ARKIV.2018.v56.n1.a9

Author

Hannes Luiro (Department of Mathematics and Statistics, University of Jyväskylä, Finland)

Abstract

It is shown for the non-centered Hardy–Littlewood maximal operator $M$ that ${\lVert DMf \rVert}_1 \: \leq C_n \: {\lVert Df \rVert}_1$ for all radial functions in $W^{1,1} (\mathbb{R}^n)$.

2010 Mathematics Subject Classification

26A45, 42B25, 46E35

Full Text (PDF format)

The author was supported by the Academy of Finland, project no. 292797.

Received 1 March 2017

Accepted 12 May 2017

Published 30 April 2018