Besov class via heat semigroup on Dirichlet spaces. III: BV functions and sub-Gaussian heat kernel estimates
From MaRDI portal
Publication:2048885
DOI10.1007/S00526-021-02041-2zbMATH Open1477.31042arXiv1903.10078OpenAlexW4233185452WikidataQ109994238 ScholiaQ109994238MaRDI QIDQ2048885
Author name not available (Why is that?)
Publication date: 24 August 2021
Published in: (Search for Journal in Brave)
Abstract: With a view toward fractal spaces, by using a Korevaar-Schoen space approach, we introduce the class of bounded variation (BV) functions in a general framework of strongly local Dirichlet spaces with a heat kernel satisfying sub-Gaussian estimates. Under a weak Bakry-'Emery curvature type condition, which is new in this setting, this BV class is identified with a heat semigroup based Besov class. As a consequence of this identification, properties of BV functions and associated BV measures are studied in detail. In particular, we prove co-area formulas, global Sobolev embeddings and isoperimetric inequalities. It is shown that for nested fractals or their direct products the BV class we define is dense in . The examples of the unbounded Vicsek set, unbounded Sierpinski gasket and unbounded Sierpinski carpet are discussed.
Full work available at URL: https://arxiv.org/abs/1903.10078
No records found.
No records found.
This page was built for publication: Besov class via heat semigroup on Dirichlet spaces. III: BV functions and sub-Gaussian heat kernel estimates
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q2048885)
