{"paper":{"title":"Exponential integrability in the spirit of Moser-Trudinger's inequalities of functions with finite non-local, non-convex energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Arka Mallick, Hoai-Minh Nguyen","submitted_at":"2019-08-16T21:16:59Z","abstract_excerpt":"Let $d \\ge 1$, $p \\ge d$, and let $\\Omega$ be a smooth bounded open subset of $\\mathbb{R}^d$. We prove some exponential integrability in the spirit of Moser-Trudinger's inequalities for measurable functions $u$ defined in $\\Omega$ such that $$ \\mathop{\\int_{\\Omega} \\int_{\\Omega}}_{|u(x) - u(y)| > \\delta} \\frac{1}{|x-y|^{d+p}} \\, dx \\, dy < + \\infty, $$ for some $\\delta > 0$. This double integral appeared in characterizations of Sobolev spaces and involved in improvements of the Sobolev inequaliies, Poincar\\'e inequalities, and Hardy inequalities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06179","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/1908.06179/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"}