Heat kernel analysis on diamond fractals Academic Article uri icon


  • This paper presents a detailed analysis of the heat kernel on an $(mathbb{N} imesmathbb{N})$-parameter family of compact metric measure spaces, which do not satisfy the volume doubling property. In particular, uniform bounds of the heat kernel and its Lipschitz continuity, as well as the continuity of the corresponding heat semigroup are studied; a specific example is presented revealing a logarithmic correction. The estimates are further applied to derive several functional inequalities of interest in describing the convergence to equilibrium of the diffusion process.

published proceedings

  • Stochastic Processes and their Applications

author list (cited authors)

  • Alonso Ruiz, P.

citation count

  • 1

complete list of authors

  • Alonso Ruiz, Patricia

publication date

  • January 2021