{"paper":{"title":"The logarithmic $p$-Laplacian on hyperbolic spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jorge J. Betancor, Lourdes Rodr\\'{\\i}guez-Mesa","submitted_at":"2026-08-02T08:26:05Z","abstract_excerpt":"In this paper, the logarithmic $p$-Laplacian operator $\\log (-\\Delta_{\\mathbb H ^n})_p$ on the hyperbolic space $\\mathbb H^n$, with $n\\geq 2$, is introduced. We prove that if $f$ is a locally Lipschitz function of exponent $\\alpha \\in (0,1)$ with compact support in $\\mathbb H^n$, then, for a suitable constant $A_{n,p}>0$, $$ \\lim_{s\\rightarrow 0^+}(-\\Delta_{\\mathbb H ^n})_p^sf(x)=A_{n,p}|f(x)|^{p-2}f(x),\\quad x\\in \\mathbb H^n, $$ where $(-\\Delta_{\\mathbb H ^n})_p^s$ denotes the $s$-fractional $p$-Laplacian on $\\mathbb H^n$. We establish a pointwise integral representation for the operator $\\lo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.01079","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/2608.01079/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"}