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The Hodge–de Rham Laplacian and Lp-boundedness of Riesz transforms on non-compact manifolds
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | CHEN, Peng | |
| 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 | OUHABAZ, El Maati | |
| dc.date.accessioned | 2024-04-04T03:20:16Z | |
| dc.date.available | 2024-04-04T03:20:16Z | |
| dc.date.issued | 2015 | |
| dc.identifier.issn | 0362-546X | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194576 | |
| dc.description.abstractEn | Let M be a complete non-compact Riemannian manifold satisfying the doubling volume property as well as a Gaussian upper bound for the corresponding heat kernel. We study the boundedness of the Riesz transform d∆ − 1 2 on both Hardy spaces H p and Lebesgue spaces L p under two different conditions on the negative part of the Ricci curvature R − . First we prove that if R − is α-subcritical for some α ∈ [0, 1), then the Riesz transform d * − → ∆ − 1 2 on differential 1-forms is bounded from the associated Hardy space H p − → ∆ (Λ 1 T * M) to L p (M) for all p ∈ [1, 2]. As a consequence, d∆ − 1 2 is bounded on L p for all p ∈ (1, p 0) where p 0 > 2 depends on α and the constant appearing in the doubling property. Second, we prove that if 1 0 |R − | 1 2 v(·, √ t) 1 p 1 p1 dt √ t + ∞ 1 |R − | 1 2 v(·, √ t) 1 p 2 p2 dt √ t < ∞, for some p 1 > 2 and p 2 > 3, then the Riesz transform d∆ − 1 2 is bounded on L p for all 1 < p < p 2 . In the particular case where v(x, r) ≥ Cr D for all r ≥ 1 and |R − | ∈ L D/2−η ∩ L D/2+η for some η > 0, then d∆ − 1 2 is bounded on L p for all 1 < p < D. Furthermore, we study the boundedness of the Riesz transform of Schrödinger operators A = ∆ + V on L p for p > 2 under conditions on R − and the potential V . We prove both positive and negative results on the boundedness of dA − 1 2 on L p . | |
| dc.description.sponsorship | Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013 | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.title.en | The Hodge–de Rham Laplacian and Lp-boundedness of Riesz transforms on non-compact manifolds | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| bordeaux.journal | Nonlinear Analysis: Theory, Methods and Applications | |
| bordeaux.page | 78-98 | |
| bordeaux.volume | 125 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01079425 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01079425v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Nonlinear%20Analysis:%20Theory,%20Methods%20and%20Applications&rft.date=2015&rft.volume=125&rft.spage=78-98&rft.epage=78-98&rft.eissn=0362-546X&rft.issn=0362-546X&rft.au=CHEN,%20Peng&MAGNIEZ,%20Jocelyn&OUHABAZ,%20El%20Maati&rft.genre=article |
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