2024/11/29 by Hugo Aimar, Ivana Gómez, Aimar, Hugo +5
Mathematics · #28A75 #28A80 #42B37 #Advanced Harmonic Analysis Research #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.2411.19856
openalex publication_date 2024/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we introduce the geometric concept of one-sided weakly porous sets in the real line and show that a set E⊂ℝ satisfies d(⋅,E)-α∈ A1+(ℝ)∩ L1_\textrmloc(ℝ) for some α>0 if and only if E is right-sided weakly porous. Furthermore, we find that the property of being both left-sided and right-sided weakly porous is equivalent to the recent weakly porous condition discussed in the bibliography, which, in turn, was previously found to be intimately related to the usual class of Muckenhoupt weights A1.