Regularity properties of Schrِdinger operators

Let L be a Schrödinger operator of the form L = − Δ + V , where the nonnegative potential V satisfies a reverse Hölder inequality. Using the method of L -harmonic extensions we study regularity estimates at the scale of adapted Hölder spaces. We give a pointwise description of L -Hölder 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.