Local lower bounds on heat kernels

Research Report MRR97-025

Local lower bounds on heat kernels

A.F.M. ter Elst and Derek W. Robinson

Abstract: We analyze convolution semigroups on a regular measure space which satisfies the local doubling property. We assume the kernels are bounded and symmetric with the characteristic small-time, volume-dependent, singularity. Then, using a weak conservation property, we deduce local lower bounds with a comparable singularity.

Applications are given to a wide range of subelliptic and strongly elliptic self-adjoint, or near self-adjoint, operators on Lie groups.

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