{"paper":{"title":"Injections de Sobolev probabilistes et applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gilles Lebeau (JAD), Nicolas Burq (LM-Orsay)","submitted_at":"2011-11-30T20:37:46Z","abstract_excerpt":"In this article, we give probabilistic versions of Sobolev embeddings on any Riemannian manifold $(M,g)$. More precisely, we prove that for natural probability measures on $L^2(M)$, almost every function belong to all spaces $L^p(M)$, $p<+\\infty$. We then give applications to the study of the growth of the $L^p$ norms of spherical harmonics on spheres $\\mathbb{S}^d$: we prove (again for natural probability measures) that almost every Hilbert base of $L^2(\\mathbb{S}^d)$ made of spherical harmonics has all its elements uniformly bounded in all $L^p(\\mathbb{S}^d), p<+\\infty$ spaces. We also prove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.7310","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":""},"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"}