{"paper":{"title":"The Fractional-Logarithmic Laplacian: Potentials, Regularity, and Critical Compact Embeddings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rui Chen","submitted_at":"2026-03-05T07:18:17Z","abstract_excerpt":"We develop potential-theoretic and \\(L^p\\)-regularity results for the fractional--logarithmic Laplacian \\((-\\Delta)^{s+\\ln}\\) and its inhomogeneous counterpart \\((\\lambda I-\\Delta)^{s+\\ln}\\), \\(\\lambda>1\\). These operators lead to logarithmic analogues of the classical Riesz and Bessel potentials. For the associated logarithmic Bessel kernel \\(K_{s+\\ln}^{\\lambda}\\), we obtain representation formulas and sharp pointwise asymptotics at both the origin and infinity, including explicit leading constants.\n  A key ingredient is a measure-level bridge between the homogeneous and inhomogeneous symbols"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.04879","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/2603.04879/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"}