Regularity estimates in H\"older spaces for Schr\"odinger operators via a T1 theorem

TL;DR

This paper establishes H"older regularity estimates for various operators related to Schr"odinger operators using a T1 theorem approach, unifying multiple regularity results in the context of potential theory.

Contribution

It introduces a unified method to derive regularity estimates for a broad class of operators associated with Schr"odinger operators using T1 theorem techniques.

Findings

Regularity estimates for maximal operators and square functions of heat and Poisson semigroups.

H"older regularity for Laplace transform multipliers and Riesz transforms.

Unified approach applicable to negative powers of Schr"odinger operators.

Abstract

We derive H\"older regularity estimates for operators associated with a time independent Schr\"odinger operator of the form $-\Delta+V$. 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 $(-\Delta+V)^{-\gamma/2}$, all of them in a unified way.