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28 p, 438.2 KB Riesz transforms associated to Schrödinger operators with negative potentials / Assaad, Joyce (Université Bordeaux 1. Institut de Mathématiques)
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. [...]
2011 - 10.5565/PUBLMAT_55111_06
Publicacions matemàtiques, Vol. 55, Núm. 1 (2011) , p. 123-150  

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