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

DOI10.1007/S11856-022-2375-6arXiv2105.15020MaRDI QIDQ6369013

Cristian González-Riquelme

Publication date: 31 May 2021

Abstract: In this paper we study a question related to the continuity of maximal operators of convolution type acting on $W^{1,1}(mathbbR)$. We prove that the map $umapsto(u^{*}{)}^{\prime }$ is continuous from $W^{1,1}(mathbbR)$ to $L^1(mathbbR)$, 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.

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

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