Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates

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

*Corresponding author for this work

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

19 Citations (Scopus)

Abstract

We introduce the class of bounded variation (BV) functions in a general framework of strictly local Dirichlet spaces with doubling measure. Under the 2-Poincaré inequality and a weak Bakry–Émery curvature type condition, this BV class is identified with the heat semigroup based Besov class B1 , 1 / 2(X) that was introduced in our previous paper. Assuming furthermore a quasi Bakry–Émery curvature type condition, we identify the Sobolev class W1 , p(X) with Bp , 1 / 2(X) for p> 1. Consequences of those identifications in terms of isoperimetric and Sobolev inequalities with sharp exponents are given.

Original languageEnglish
Article number103
JournalCalculus of Variations and Partial Differential Equations
Volume59
Issue3
ISSN0944-2669
DOIs
Publication statusPublished - 1 Jun 2020
Externally publishedYes

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