Heat kernels of multiplicative perturbations: Holder estimates and Gaussian lower bounds

Abstract

We study in an abstract setting heat kernels of multiplicative perturbations bA where b is a bounded measurable function.Our aim is to show that Hölder estimates and Gaussian lower bounds carry over from the heat kernel of A to the heat kernel of bA.In preparing these results we show that Hölder continuity estimates of heat kernels can be characterized in terms of Gagliardo-Nirenberg type inequalities.