The one-dimensional centred maximal function diminishes the variation of indicator functions
Classical Analysis and ODEs
2021-07-28 v1
Abstract
We prove sharp local and global variation bounds for the centred Hardy--Littlewood maximal functions of indicator functions in one dimension. We characterise maximisers, treat both the continuous and discrete settings and extend our results to a larger class of functions.
Cite
@article{arxiv.2107.12404,
title = {The one-dimensional centred maximal function diminishes the variation of indicator functions},
author = {Constantin Bilz and Julian Weigt},
journal= {arXiv preprint arXiv:2107.12404},
year = {2021}
}
Comments
18 pages, 3 figures