Heat Kernel And Riesz Transform Of Schrodinger Operators

TL;DR

This paper establishes Gaussian bounds for the heat kernel of Schrödinger operators with decaying potentials and proves sharp boundedness results for the associated Riesz transform, also exploring p-hyperbolicity.

Contribution

It provides new Gaussian estimates for heat kernels and sharp boundedness results for Riesz transforms of Schrödinger operators with small-at-infinity potentials.

Findings

Gaussian estimates for heat kernel of Schrödinger operators

Boundedness of Riesz transform with potential

Characterization of p-hyperbolicity

Abstract

The goal of this article is twofold: in a first part, we prove Gaussian estimates for the heat kernel of Schr{\"o}dinger operators delta + V whose potential V is "small at infinity" in an integral sense. In a second part, we prove sharp boundedness result for the associated Riesz transform with potential d(delta+V) --1/2. A characterization of p-hyperbolicity, which is of independent interest, is also proved.