L p -estimates for the heat semigroup on differential forms, and related problems
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | MAGNIEZ, Jocelyn | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | MAATI OUHABAZ, El | |
| dc.date.accessioned | 2024-04-04T03:10:08Z | |
| dc.date.available | 2024-04-04T03:10:08Z | |
| dc.date.created | 2015 | |
| dc.date.issued | 2020 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193664 | |
| dc.description.abstractEn | We 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.iso | en | |
| dc.title.en | L p -estimates for the heat semigroup on differential forms, and related problems | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s12220-019-00188-1 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.identifier.arxiv | 1705.06945 | |
| bordeaux.journal | Journal of Geometric Analysis | |
| bordeaux.page | 3002-3025 | |
| bordeaux.volume | 30 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 3 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01524855 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01524855v1 | |
| bordeaux.COinS | ctx_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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