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arXiv · 1911.00065

Regularity of the centered fractional maximal function on radial functions

David Beltran·José Madrid
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Abstract

We study the regularity properties of the centered fractional maximal function $M_β$. More precisely, we prove that the map $f \mapsto |\nabla M_βf|$ is bounded and continuous from $W^{1,1}(\mathbb{R}^d)$ to $L^q(\mathbb{R}^d)$ in the endpoint case $q=d/(d-β)$ if $f$ is radial function. For $d=1$, the radiality assumption can be removed. This corresponds to the counterparts of known results for the non-centered fractional maximal function. The main new idea consists in relating the centered and non-centered fractional maximal function at the derivative level.

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David Beltran, José Madrid. 2019-10-31. Regularity of the centered fractional maximal function on radial functions. https://arxiv.org/abs/1911.00065

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