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L p -estimates for the heat semigroup on differential forms, and related problems

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMAGNIEZ, Jocelyn
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMAATI OUHABAZ, El
dc.date.accessioned2024-04-04T03:10:08Z
dc.date.available2024-04-04T03:10:08Z
dc.date.created2015
dc.date.issued2020
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193664
dc.description.abstractEnWe consider a complete non-compact Riemannian manifold satisfying the volume doubling property and a Gaussian upper bound for its heat kernel (on functions). Let − → ∆ k be the Hodge-de Rham Laplacian on differential k-forms with k ≥ 1. By the Bochner decomposition formula − → ∆ k = * + R k. Under the assumption that the negative part R − k is in an enlarged Kato class, we prove that for all p ∈ [1, ∞], e −t − → ∆ k p−p ≤ C(t log t) D 4 (1− 2 p) (for large t). This estimate can be improved if R − k is strongly sub-critical. In general, (e −t − → ∆ k) t>0 is not uniformly bounded on L p for any p = 2. We also prove the gradient estimate e −t∆ p−p ≤ Ct − 1 p , where ∆ is the Laplace-Beltrami operator (acting on functions). Finally we discuss heat kernel bounds on forms and the Riesz transform on L p for p > 2.
dc.language.isoen
dc.title.enL p -estimates for the heat semigroup on differential forms, and related problems
dc.typeArticle de revue
dc.identifier.doi10.1007/s12220-019-00188-1
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.identifier.arxiv1705.06945
bordeaux.journalJournal of Geometric Analysis
bordeaux.page3002-3025
bordeaux.volume30
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue3
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01524855
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01524855v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Geometric%20Analysis&rft.date=2020&rft.volume=30&rft.issue=3&rft.spage=3002-3025&rft.epage=3002-3025&rft.au=MAGNIEZ,%20Jocelyn&MAATI%20OUHABAZ,%20El&rft.genre=article


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