Weakly porous sets and Muckenhoupt Ap distance functions

• Published in: Journal of functional analysis Vol. 287; no. 8
• Main Authors: Anderson, Theresa C., Lehrbäck, Juha, Mudarra, Carlos, Vähäkangas, Antti V.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.10.2024
• Subjects: Distance function; Fractals; Muckenhoupt weight; Weak porosity; 42B99; 28A75; 42B25; Distance function; 28A80; Weak porosity; Muckenhoupt weight; Fractals

We consider 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...