Gaussian estimates for Schrödinger perturbations
Tom 221 / 2014
Studia Mathematica 221 (2014), 151-173 MSC: Primary 47D06, 47D08; Secondary 35A08, 35B25. DOI: 10.4064/sm221-2-4
We propose a new general method of estimating Schrödinger perturbations of transition densities using an auxiliary transition density as a majorant of the perturbation series. We present applications to Gaussian bounds by proving an optimal inequality involving four Gaussian kernels, which we call the 4G Theorem. The applications come with honest control of constants in estimates of Schrödinger perturbations of Gaussian-type heat kernels and also allow for specific non-Kato perturbations.