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

Authors: El Maati Ouhabaz

Issue: Volume 47 (1998), Issue 4, 1481-1496

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 H\"older 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 H\"older continuity estimates of heat kernels can be characterized in terms of Gagliardo-Nirenberg type inequalities.