Weakly porous sets and Muckenhoupt Ap distance functions
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
Julkaistu sarjassa
Journal of Functional AnalysisPäivämäärä
2024Tekijänoikeudet
© 2024 the Authors
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 < ∞.
Julkaisija
ElsevierISSN Hae Julkaisufoorumista
0022-1236Asiasanat
Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/233283945
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Suomen AkatemiaRahoitusohjelmat(t)
Akatemiahanke, SALisätietoja rahoituksesta
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).Lisenssi
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