{"paper":{"title":"One-sided median porous sets and one-sided Muckenhoupt distance functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alptekin Can Goksan, Ignacio Uriarte-Tuero","submitted_at":"2026-07-01T16:54:30Z","abstract_excerpt":"We introduce the notion of one-sided median porosity for subsets $E$ of $\\mathbb{R}$. We prove that this condition is necessary and sufficient for the distance weight $d_E^{-\\alpha}$ to belong to a one-sided Muckenhoupt $A_p$ class for some $\\alpha>0$ and $1<p<\\infty$. As part of the proof, we obtain new characterizations of one-sided $A_p$ weights and one-sided $\\mathrm{BMO}$ functions, in terms of medians. It was recently shown that $d_E^{-\\alpha}$ is a one-sided Muckenhoupt $A_1$ weight for some $\\alpha>0$ if and only if $E$ is one-sided weakly porous. In this paper, we find the precise ran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01167","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.01167/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}