Riesz transforms associated to Schrödinger operators with negative potentials

Joyce Assaad (1)

1 IMB - Institut de Mathématiques de Bordeaux

The goal of this paper is to study the Riesz transforms $\na A^{-1/2}$ where $A$ is the Schr\"{o}dinger operator $-\D-V,\ \ V\ge 0$, under different conditions on the potential $V$. We prove that if $V$ is strongly subcritical, $\na A^{-1/2}$ is bounded on $L^p(\R^N)$ , $N\ge3$, for all $p\in(p_0';2]$ where $p_0'$ is the dual exponent of $p_0$ where $2<\frac{2N}{N-2}

Mots clés: Riemannian manifolds; Riesz transforms; Schrödinger operators; off-diagonal estimates; singular operators; Riemannian manifolds.

Domaines: Analyse fonctionnelle [math.FA]

Joyce Assaad. Riesz transforms associated to Schrödinger operators with negative potentials. 2009. ⟨hal-00382824v2⟩