{"paper":{"title":"Local and non-local $p$-energies on metric measure spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA","math.MG","math.PR"],"primary_cat":"math.AP","authors_text":"Meng Yang","submitted_at":"2026-02-11T16:15:44Z","abstract_excerpt":"For $p>1$, we study subordination phenomena for local and non-local regular $p$-energies on metric measure spaces. Under suitable geometric assumptions, we show that if a local regular $p$-energy satisfies a Poincar\\'e inequality and a cutoff Sobolev inequality with scaling function $\\Psi$, then any non-local $p$-form induced by a jumping kernel with scaling function $\\Upsilon$, where $\\Upsilon$ lies strictly above $\\Psi$ at small scales, defines a regular $p$-energy satisfying a non-local Poincar\\'e inequality and a non-local cutoff Sobolev inequality. The corresponding scaling function $\\Xi$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.10990","kind":"arxiv","version":2},"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/2602.10990/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"}