Hardy inequalities and Assouad dimensions
Functional Analysis
2017-04-14 v3 Classical Analysis and ODEs
Abstract
We establish both sufficient and necessary conditions for weighted Hardy inequalities in metric spaces in terms of Assouad (co)dimensions. Our sufficient conditions in the case where the complement is thin are new even in Euclidean spaces, while in the case of a thick complement we give new formulations for previously known sufficient conditions which reveal a natural duality between these two cases. Our necessary conditions are rather straight-forward generalizations from the unweighted case, but together with some examples they indicate the essential sharpness of our results. In addition, we consider the mixed case where the complement may contain both thick and thin parts.
Cite
@article{arxiv.1402.6134,
title = {Hardy inequalities and Assouad dimensions},
author = {Juha Lehrbäck},
journal= {arXiv preprint arXiv:1402.6134},
year = {2017}
}
Comments
23 pages. Minor revisions to the previous versions