Riesz transforms of Schrödinger operators on manifolds
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ASSAAD, Joyce | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | OUHABAZ, El Maati | |
| dc.date.accessioned | 2024-04-04T02:18:06Z | |
| dc.date.available | 2024-04-04T02:18:06Z | |
| dc.date.created | 2012 | |
| dc.date.issued | 2012 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189283 | |
| dc.description.abstractEn | We consider Schrödinger operators A = − + V on Lp(M) where M is a complete Riemannian manifold of homogeneous type and V = V + − V − is a signed potential. We study boundedness of Riesz transform type operators ∇A −1 2 and |V |12 A −12 on Lp(M). When V − is strongly subcritical with constant α ∈ (0, 1) we prove that such operators are bounded on Lp(M) for p ∈ (p 0, 2] where p 0 = 1 if N ≤ 2, and p 0 = ( 2N (N−2)(1− √ 1−α) ) ∈ (1, 2) if N > 2. We also study the case p >2. With additional conditions on V and M we obtain boundedness of ∇A −1/2 and |V |1/2A −1/2 on Lp(M) for p ∈ (1, inf(q1,N)) where q1 is such that ∇(− ) −1 2 is bounded on Lr(M) for r ∈ [2, q1). | |
| dc.language.iso | en | |
| dc.subject.en | Riesz transforms | |
| dc.subject.en | Schrödinger operators | |
| dc.subject.en | Riemannian manifolds | |
| dc.subject.en | Singular operators | |
| dc.subject.en | Off-diagonal estimates | |
| dc.title.en | Riesz transforms of Schrödinger operators on manifolds | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s12220-011-9231-y | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| bordeaux.journal | Journal of Geometric Analysis | |
| bordeaux.page | 1108-1136 | |
| bordeaux.volume | 22 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 4 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00992214 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00992214v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Geometric%20Analysis&rft.date=2012&rft.volume=22&rft.issue=4&rft.spage=1108-1136&rft.epage=1108-1136&rft.au=ASSAAD,%20Joyce&OUHABAZ,%20El%20Maati&rft.genre=article |
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