{"paper":{"title":"Bounds for the maximal and Riesz potential operators with variable fractionality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Francisco Gon\\c{c}alves, Tuomas Oikari","submitted_at":"2026-07-01T15:29:40Z","abstract_excerpt":"We prove $L^{p(\\cdot)}$-to-$L^{q(\\cdot)}$ bounds for variable versions of the fractional maximal $M^{\\alpha(\\cdot)}$ and Riesz potential $I^{\\alpha(\\cdot)}$ operators. The changing fractionality in these operators is given by averaging the function $\\alpha(\\cdot)$ over balls. The bounds for $M^{\\alpha(\\cdot)}$ are in terms of a three-exponent Muckenhoupt condition relating $p(\\cdot),q(\\cdot),$ and $\\alpha(\\cdot)$, while the bounds for $I^{\\alpha(\\cdot)}$ are in terms of the boundedness of $M^{\\alpha(\\cdot)}$ and a packing condition on $\\alpha(\\cdot).$ These bounds hold under Hardy--Littlewood "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.01069","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/2607.01069/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"}