arXiv Analytics

Sign in

arXiv:2109.09691 [math.CA]AbstractReferencesReviewsResources

Continuity for the one-dimensional centered Hardy-Littlewood maximal operator at the derivative level

Cristian González-Riquelme

Published 2021-09-20Version 1

We prove the continuity of the map $f \mapsto (Mf)'$ from $W^{1,1}(\mathbb{R})$ to $L^1(\mathbb{R})$, where $M$ is the centered Hardy-Littlewood maximal operator. This solves a question posed by Carneiro, Madrid and Pierce.

Comments: 10 pages. 2 figures
Categories: math.CA
Subjects: 42B25, 46E35
Related articles: Most relevant | Search more
arXiv:1207.2710 [math.CA] (Published 2012-07-11, updated 2013-01-04)
Medians, Continuity, and Oscillation
arXiv:2105.15020 [math.CA] (Published 2021-05-31)
On the continuity of maximal operators of convolution type at the derivative level
arXiv:2102.10206 [math.CA] (Published 2021-02-19)
Continuity of the gradient of the fractional maximal operator on $W^{1,1}(\mathbb{R}^d)$

Links

Toolbox