BV functions and fractional Laplacians on Dirichlet spaces

Alexander Teplyaev; Fabrice Baudoin; Li Chen; Luke Rogers; Nageswari Shanmugalingam; Patricia Alonso Ruiz

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BV functions and fractional Laplacians on Dirichlet spaces

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arxiv 1910.13330 v1 pith:PS3QODO4 submitted 2019-10-28 math.MG math-phmath.FAmath.MPmath.PR

BV functions and fractional Laplacians on Dirichlet spaces

Patricia Alonso Ruiz , Fabrice Baudoin , Li Chen , Luke Rogers , Nageswari Shanmugalingam , Alexander Teplyaev This is my paper

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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.

BV functions and fractional Laplacians on Dirichlet spaces

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