Regularity properties of Schrodinger operators

Let L be a Schrodinger operator of the form L = -del + V, where the nonnegative potential V satisfies a reverse Holder inequality. Using the method of L-harmonic extensions we study regularity estimates at the scale of adapted Holder spaces. We give a pointwise description of L-Holder spaces and provide some characterizations in terms of the growth of fractional derivatives of any order and Carleson measures. Applications to fractional powers of L and multipliers of Laplace transform type developed. (C) 2011 Elsevier Inc. All rights reserved.