Weighted norm inequalities in a bounded domain by the sparse domination method
Analysis of PDEs
2020-05-01 v2
Abstract
We prove a local two-weight Poincar\'e inequality for cubes using the sparse domination method that has been influential in harmonic analysis. The proof involves a localized version of the Fefferman--Stein inequality for the sharp maximal function. By establishing a local-to-global result in a bounded domain satisfying a Boman chain condition, we show a two-weight -Poincar\'e inequality in such domains. As an application we show that certain nonnegative supersolutions of the -Laplace equation and distance weights are -admissible in a bounded domain, in the sense that they support versions of the -Poincar\'e inequality.
Cite
@article{arxiv.1910.06839,
title = {Weighted norm inequalities in a bounded domain by the sparse domination method},
author = {Emma-Karoliina Kurki and Antti V. Vähäkangas},
journal= {arXiv preprint arXiv:1910.06839},
year = {2020}
}