Regularity estimates in Hölder spaces for Schrödinger operators via a T1 theorem

Abstract

We derive Hölder regularity estimates for operators associated with a time-independent Schrödinger operator of the form -Δ+V. The results are obtained by checking a certain condition on the function T1. Our general method applies to get regularity estimates for maximal operators and square functions of the heat and Poisson semigroups, for Laplace transform type multipliers and also for Riesz transforms and negative powers (-Δ+V)-γ/2, all of them in a unified way. © 2012 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag.