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Riesz transforms associated to Schrödinger operators with negative potentials
Assaad, Joyce (Université Bordeaux 1. Institut de Mathématiques)

Data: 2011
Resum: 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.
Drets: Tots els drets reservats
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Matèria: Riesz transforms ; Schrödinger operators ; off-diagonal estimates ; Singular operators ; Riemannian manifolds
Publicat a: Publicacions Matemàtiques, Vol. 55, Núm. 1 (2011) , p. 123-150, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_55111_06

28 p, 438.2 KB

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