Weakly porous sets and Muckenhoupt Ap distance functions
Abstract
We examine the class of weakly porous sets in Euclidean spaces. As our first main result we show that the distance weight w(x)=dist(x,E)−α belongs to the Muckenhoupt class A1, for some α>0, if and only if E⊂Rn is weakly porous. We also give a precise quantitative version of this characterization in terms of the so-called Muckenhoupt exponent of E. When E is weakly porous, we obtain a similar quantitative characterization of w∈Ap, for 1 < p < ∞, as well. At the end of the paper, we give an example of a set E⊂R which is not weakly porous but for which w∈Ap∖A1 for every 0<α<1 and 1 < p < ∞.
Main Authors
Format
Articles
Research article
Published
2024
Series
Subjects
Publication in research information system
Publisher
Elsevier
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202408165528Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
0022-1236
DOI
https://doi.org/10.1016/j.jfa.2024.110558
Language
English
Published in
Journal of Functional Analysis
Citation
- Anderson, T. C., Lehrbäck, J., Mudarra, C., & Vähäkangas, A. V. (2024). Weakly porous sets and Muckenhoupt Ap distance functions. Journal of Functional Analysis, 287(8), Article 110558. https://doi.org/10.1016/j.jfa.2024.110558
License
Funder(s)
Research Council of Finland
Funding program(s)
Academy Project, AoF
Akatemiahanke, SA
Additional information about funding
T.C.A. was supported in part by an NSF graduate research fellowship, NSF DMS-2231990 and NSP DMS-1954407. She thanks Tuomas Hytönen for an invitation to visit the University of Helsinki where this project originated. C.M. was supported by the Academy of Finland via the projects Geometric Aspects of Sobolev Space Theory (grant No. 314789) and Incidences on Fractals (grant No. 321896).
Copyright© 2024 the Authors