BV functions and Besov spaces associated with Dirichlet spaces

TL;DR

This paper develops a unified theory of BV functions and Besov spaces within abstract Dirichlet spaces, extending known frameworks and applying to new contexts such as fractals.

Contribution

It introduces a general framework for BV and Besov spaces in Dirichlet spaces, encompassing existing examples and enabling analysis on fractals and other complex structures.

Findings

Unified theory applicable to various Dirichlet spaces

Extension of BV and Besov spaces to fractals

Framework facilitates analysis on complex geometric structures

Abstract

We develop a theory of bounded variation functions and Besov spaces in abstract Dirichlet spaces which unifies several known examples and applies to new situations, including fractals.