46 citations · 339 across the 63 of their papers we have counts for
10 papers · 1 filter
Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates
Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen +3
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 we…
Besov class via heat semigroup on Dirichlet spaces I: Sobolev type inequalities
Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen +3
We introduce heat semigroup-based Besov classes in the general framework of Dirichlet spaces. General properties of those classes are studied and quantitative regularization estima…
Asymptotic behavior of BV functions and sets of finite perimeter in metric measure spaces
Sylvester Eriksson-Bique, James T. Gill, Panu Lahti +1
In this paper, we study the asymptotic behavior of BV functions in complete metric measure spaces equipped with a doubling measure supporting a -Poincaré inequality. We show tha…
The Liouville theorem for -harmonic functions and quasiminimizers with finite energy
Anders Björn, Jana Björn, Nageswari Shanmugalingam
We show that, under certain geometric conditions, there are no nonconstant quasiminimizers with finite th power energy in a (not necessarily complete) metric measure space equip…
Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a -Poincaré inequality
Estibalitz Durand-Cartagena, Sylvester Eriksson-Bique, Riikka Korte +1
We consider two notions of functions of bounded variation in complete metric measure spaces, one due to Martio and the other due to Miranda~Jr. We show that these two notions coinc…
The prime end capacity of inaccessible prime ends, resolutivity, and the Kellogg property
Tomasz Adamowicz, Nageswari Shanmugalingam
Prime end boundaries of domains are studied in the setting of complete doubling metric measure spaces supporting a -Poincaré inequality. Notions of rectifiably…
Locally -admissible measures on
Anders Bjorn, Jana Bjorn, Nageswari Shanmugalingam
In this note we show that locally -admissible measures on necessarily come from local Muckenhoupt weights. In the proof we employ the corresponding characteri…
Modulus of families of sets of finite perimeter and quasiconformal maps between metric spaces of globally -bounded geometry
Rebekah Jones, Panu Lahti, Nageswari Shanmugalingam
We generalize a result of J. C. Kelly to the setting of Ahlfors -regular metric measure spaces supporting a -Poincaré inequality. It is shown that if and are two Ahlf…
BV functions and Besov spaces associated with Dirichlet spaces
Patricia Alonso-Ruiz, Fabrice Baudoin, Li Chen +3
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 fract…
Infinity modulus and the essential metric
Nathan Albin, Jared Hoppis, Pietro Poggi-Corradini +1
We study -modulus on general metric spaces and establish its relation to shortest lengths of paths. This connection was already known for modulus on graphs, but the formula…