The variation of the maximal function of a radial function

Hannes Luiro

doi:10.4310/ARKIV.2018.v56.n1.a9

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Home > Journals > Ark. Mat. > Volume 56 > Issue 1 > Article

April 2018 The variation of the maximal function of a radial function

Hannes Luiro

Author Affiliations +

Hannes Luiro¹
¹Department of Mathematics and Statistics, University of Jyväskylä, Finland

Ark. Mat. 56(1): 147-161 (April 2018). DOI: 10.4310/ARKIV.2018.v56.n1.a9

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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 $W^{1,1} (\mathbb{R}^n)$.

Funding Statement

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

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Hannes Luiro. "The variation of the maximal function of a radial function." Ark. Mat. 56 (1) 147 - 161, April 2018. https://doi.org/10.4310/ARKIV.2018.v56.n1.a9