Fractional Poincar\'e and localized Hardy inequalities on metric spaces
Classical Analysis and ODEs
2021-08-17 v1 Analysis of PDEs
Abstract
We prove fractional Sobolev-Poincar\'e inequalities, capacitary versions of fractional Poincar\'e inequalities, and pointwise and localized fractional Hardy inequalities in a metric space equipped with a doubling measure. Our results generalize and extend earlier work where such inequalities have been considered in the Euclidean spaces or in the non-fractional setting in metric spaces. The results concerning pointwise and localized variants of fractional Hardy inequalities are new even in the Euclidean case.
Keywords
Cite
@article{arxiv.2108.07209,
title = {Fractional Poincar\'e and localized Hardy inequalities on metric spaces},
author = {Bartłomiej Dyda and Juha Lehrbäck and Antti V. Vähäkangas},
journal= {arXiv preprint arXiv:2108.07209},
year = {2021}
}