Besov class via heat semigroup on Dirichlet spaces I: Sobolev type inequalities

Patricia Alonso Ruiz, Fabrice Baudoin*, Li Chen, Luke G. Rogers, Nageswari Shanmugalingam, Alexander Teplyaev

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

21 Citations (Scopus)

Abstract

We introduce heat semigroup-based Besov classes in the general framework of Dirichlet spaces. General properties of those classes are studied and quantitative regularization estimates for the heat semigroup in this scale of spaces are obtained. As a highlight of the paper, we obtain a far reaching Lp-analogue, p≥1, of the Sobolev inequality that was proved for p=2 by N. Varopoulos under the assumption of ultracontractivity for the heat semigroup. The case p=1 is of special interest since it yields isoperimetric type inequalities.

Original languageEnglish
Article number108459
JournalJournal of Functional Analysis
Volume278
Issue11
ISSN0022-1236
DOIs
Publication statusPublished - 15 Jun 2020
Externally publishedYes

Keywords

  • Besov space
  • Dirichlet space
  • Heat kernel
  • Sobolev inequality

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