Regularity properties of Schr\"odinger operators

Let L be a Schr\"odinger operator of the form L=-\Delta+V, where the nonnegative potential V satisfies a reverse H\"older inequality. Using the method of L-harmonic extensions we study regularity estimates at the scale of adapted H\"older spaces. We give a pointwise description of L-H\"older 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.