Poincar\'e inequalities for the maximal function
Classical Analysis and ODEs
2021-02-23 v2
Abstract
We study generalized Poincar\'e inequalities. We prove that if a function satisfies a suitable inequality of Poincar\'e type, then the Hardy-Littlewood maximal function also obeys a meaningful estimate of similar form. As a by-product, we get a unified approach to proving that the maximal operator is bounded on Sobolev, Lipschitz and BMO spaces.
Cite
@article{arxiv.1605.05176,
title = {Poincar\'e inequalities for the maximal function},
author = {Olli Saari},
journal= {arXiv preprint arXiv:1605.05176},
year = {2021}
}
Comments
19 pages, 1 figure, a change in the abstract and a mistake removed. The application to $W^{1,1}$ reproduces the known results but does not improve them. All theorems remain as they were