Riesz transforms associated to Schrödinger operators with negative potentials
The goal of this paper is to study the Riesz transforms ∇ A-1/2 where A is the Schrödinger operator - ∆ - V, V ≥ 0, under different conditions on the potential V . We prove that if V is strongly subcritical, ∇ A-1/2 is bounded on Lp(RN), N ≥ 3, for all p є (p'0 ; 2] where p'0 is the dual e...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:65201 |
| Acceso en línea: | https://ddd.uab.cat/record/65201 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_55111_06 |
| Access Level: | acceso abierto |
| Palabra clave: | Riesz transforms Schrödinger operators Off-diagonal estimates Singular operators Riemannian manifolds |
| Sumario: | The goal of this paper is to study the Riesz transforms ∇ A-1/2 where A is the Schrödinger operator - ∆ - V, V ≥ 0, under different conditions on the potential V . We prove that if V is strongly subcritical, ∇ A-1/2 is bounded on Lp(RN), N ≥ 3, for all p є (p'0 ; 2] where p'0 is the dual exponent of p0 where 2 < 2N/N-2 < p0 < ∞; and we give a counterexample to the boundedness on Lp (RN) for p є (1;p'0) ∪ (p0*;∞) where p0* :=poN/N+po is the reverse Sobolev exponent of p0. If the potential is strongly subcritical in the Kato subclass K∞/N, then ∇ A-1/2 is bounded on Lp (RN) for all p є (1;2], moreover if it is in LN/w/2 (RN) then ∇ A-1/2 is bounded on Lp (RN) for all p є (1;N). We prove also boundedness of V1/2 A-1/2 with the same conditions on the same spaces. Finally we study these operators on manifolds. We prove that our results hold on a class of Riemannian manifolds. |
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