Weighted inequalities of Fefferman-Stein type for Riesz-Schrödinger transforms

Abstract

In this work we are concerned with Fefferman-Stein type inequalities. More precisely, given an operator T and some p, 1 < p < ∞, we look for operators M such that the inequality |+ |T f |pw < C | | f |pM w, holds true for any weight w. Specifically, we are interested in the case of T being any first or second order Riesz transform associated to the Schrödinger operator L = −Δ + V , with V a non-negative function satisfying an appropriate reverse-Hölder condition. For the Riesz-Schrödinger transforms ∇L−1/2 and ∇2 L−1 we make use of a result due to C. Pérez where this problem is solved for classical Calderón-Zygmund operators.