Weak porosity in spaces of homogeneous type

Le résumé fourni par la source

Based on the theory of Muckenhoupt weights, short and conceptually simpler proofs are provided for the following two implications: (1) if $(X, d, μ)$ is a space of homogeneous type where $d$-balls are open sets and the Lebesgue differentiation theorem holds true and if $E \subset X$ is a weakly porous set whose maximal $E$-free hole function $ρ_{d, E}$ is doubling, then $\dist{\cdot, E}^{-α} \in A_1(X, d, μ)$ for some $α> 0$; and (2) now without the assumption on the validity of Lebesgue's differentiation theorem, if $\dist{\cdot, E}^{-α} \in A_1(X, d, μ)$ for some $α> 0$, then $ρ_{d, E}$ is doubling.

Ce résumé expose les affirmations des auteurs. BNTIC ne l’interprète pas comme une validation indépendante des résultats.