Hardy inequalities and Assouad dimensions
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, indicate the essential sharpness of our results. In addition, we consider the mixed case in which the complement may contain both thick and thin parts.
Main Author
Format
Articles
Research article
Published
2017
Series
Subjects
Publication in research information system
Publisher
Hebrew University Magnes Press; Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201906253430Use this for linking
Review status
Peer reviewed
ISSN
0021-7670
DOI
https://doi.org/10.1007/s11854-017-0013-8
Language
English
Published in
Journal d'Analyse Mathématique
Citation
- Lehrbäck, J. (2017). Hardy inequalities and Assouad dimensions. Journal d'Analyse Mathématique, 131(1), 367-398. https://doi.org/10.1007/s11854-017-0013-8
License
Copyright© Hebrew University Magnes Press 2017