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

```@article{Ruiz2020BesovCV,
title={Besov class via heat semigroup on Dirichlet spaces I: Sobolev type inequalities},
author={Patricia Alonso Ruiz and Fabrice Baudoin and Li Chen and Luke G. Rogers and Nageswari Shanmugalingam and Alexander Teplyaev},
journal={Journal of Functional Analysis},
year={2020}
}```
• Published 10 November 2018
• Mathematics
• Journal of Functional Analysis
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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
BV functions and fractional Laplacians on Dirichlet spaces
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