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

Abstract

Abstract. We derive Hölder regularity estimates for operators associated with a time independent Schrödinger operator of the form −∆ + V . The results are obtained by checking a certain condition on the function T 1. 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 (−∆ + V ) −γ/2 , all of them in a unified way.

Variation and oscillation operators on weighted Morrey–Campanato spaces in the Schrödinger setting

“…Harmonic analysis associated with the operator L has been developed by several authors in the last century. Shen's paper [42] can be considered the starting point of the most of these studies (see, for instance, [24], [25], [26], [31], [35], [43] and [48]). Professor Eleonor Harboure, to whose memory this paper is dedicated, studied several important aspects of the harmonic analysis in the Schrödinger setting ([2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [18] and [27]).…”