Heat kernel analysis on diamond fractals

Patricia Alonso Ruiz

Published 2019-06-14Version 1

This paper presents a detailed analysis of the heat kernel on an $(\mathbb{N}\times\mathbb{N})$-parameter family of compact metric measure spaces, which do not satisfy the volume doubling property. In particular, the Lipschitz continuity of the heat kernel and the continuity of the corresponding heat semigroup are studied. Explicit bounds for the time-dependent Lipschitz constants are provided and an specific example is computed, where a logarithmic correction appear. The estimates are further applied to derive several functional inequalities of interest in describing the convergence to equilibrium of the diffusion process.