Local Lower Bounds on Heat Kernels

摘要

We analyze convolution semigroups on a regular measure space which satisfies the211u001elocal doubling property. We assume the kernels are bounded and symmetric with the 211u001echaracteristic small-time, volume-dependent, singularity. Then, using a weak 211u001econservation property, we deduce local lower bounds with a comparable 211u001esingularity. Applications are given to a wide range of subelliptic and strongly 211u001eelliptic self-adjoint, or near self-adjoint, operators on Lie groups.