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arXiv · 2105.15020

On the continuity of maximal operators of convolution type at the derivative level

Cristian González-Riquelme
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Abstract

In this paper we study a question related to the continuity of maximal operators of convolution type acting on $W^{1,1}(\mathbb{R})$. We prove that the map $u\mapsto (u^{*})'$ is continuous from $W^{1,1}(\mathbb{R})$ to $L^{1}(\mathbb{R})$, where $u^{*}$ is the maximal function associated to the Poisson kernel, the Heat kernel or a family of kernels related to the fractional Laplacian. This is the first result of this type for a centered maximal operator.

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Cristian González-Riquelme. 2021-05-31. On the continuity of maximal operators of convolution type at the derivative level. https://arxiv.org/abs/2105.15020

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