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Register a new userOn master test plans for the space of BV functions
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We prove that on an arbitrary metric measure space a countable collection of test plans is sufficient to recover all $rm BV$ functions and their total variation measures. In the setting of non-branching ${sf CD}(K,N)$ spaces (with finite reference measure), we can additionally require these test plans to be concentrated on geodesics.
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We study $L^p$ Besov critical exponents and isoperimetric and Sobolev inequalities associated with fractional Laplacians on metric measure spaces. The main tool is the theory of heat semigroup based Besov classes in Dirichlet spaces that was introduced by the authors in previous works.
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