BV functions and Besov spaces associated with Dirichlet spaces
Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen, Luke Rogers, Nageswari, Shanmugalingam, Alexander Teplyaev

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.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Mathematical Analysis and Transform Methods · Mathematical Dynamics and Fractals
