Small time characterization of heat kernels in a weighted setting

Abstract

We provide a small time characterization for the Gaussian bounds on the heat kernel of the C0-semigroup generated by a second-order degenerate elliptic operator on the weighted Lebesgue space Lw2(Rd), where w belongs to the class A1 of Muckenhoupt weights. The result extends (Elst in Proc Am Math Soc 134:707–714, 2005, Thereom 1) to a weighted setting.