Title: Fractional Integral Operators Associated to Schrodinger Operators

Abstract: Consider the Schroedinger operator Lf(x) = – Laplace f(x) + V(x)f(x). We investigate weighted inequalities for the fractional integral operator I_a = (L)^-a/2. More precisely, let 0 < a < n and 1/p – 1/q = a/n, we would like to estimate the operator norm of I_a as an operator from L^p(w^p) to L^q(w^q) in terms of a fractional Muckenhoupt condition adapted to L. I_a has better decay properties than the classical fractional integral operator but is highly “non-local”; this is one of the obstructions to establishing the weighted estimate.