{"paper":{"title":"Self-improvement of fractional Hardy inequalities in metric measure spaces via hyperbolic fillings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CA","math.MG"],"primary_cat":"math.AP","authors_text":"Josh Kline, Sylvester Eriksson-Bique","submitted_at":"2024-12-03T21:26:14Z","abstract_excerpt":"In this paper, we prove a self-improvement result for $(\\theta,p)$-fractional Hardy inequalities, in both the exponent $1<p<\\infty$ and the regularity parameter $0<\\theta<1$, for bounded domains in doubling metric measure spaces. The key conceptual tool is a Caffarelli-Silvestre-type argument, which relates fractional Sobolev spaces on $Z$ to Newton-Sobolev spaces in the hyperbolic filling $\\overline{X}_{\\varepsilon}$ of $Z$ via trace results. Using this insight, it is shown that a fractional Hardy inequality in an open subset of $Z$ is equivalent to a classical Hardy inequality in the filling"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.02848","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/2412.02848/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"}