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

We study in an abstract setting heat kernels of multiplicative perturbation s bA where b is a bounded measurable function. Our aim is to show that Hold er 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 Holder c ontinuity estimates of heat kernels can be characterized in terms of Gaglia rdo-Nirenberg type inequalities.