Maximal function estimates and self-improvement results for Poincar\'e inequalities
Classical Analysis and ODEs
2017-05-16 v1 Analysis of PDEs
Abstract
Our main result is an estimate for a sharp maximal function, which implies a Keith-Zhong type self-improvement property of Poincar\'e inequalities related to differentiable structures on metric measure spaces. As an application, we give structure independent representation for Sobolev norms and universality results for Sobolev spaces.
Cite
@article{arxiv.1705.05072,
title = {Maximal function estimates and self-improvement results for Poincar\'e inequalities},
author = {Juha Kinnunen and Juha Lehrbäck and Antti V. Vähäkangas and Xiao Zhong},
journal= {arXiv preprint arXiv:1705.05072},
year = {2017}
}