46 citations · 339 across the 63 of their papers we have counts for
10 papers · 1 filter
On the equivalence of BV notions in metric measure spaces
Luigi Ambrosio, Enrico Pasqualetto, Nageswari Shanmugalingam
The aim of the paper is to compare in detail several notions of space of functions of bounded variation in metric measure spaces . Informall…
Finite dimensionality of Besov spaces and potential-theoretic decomposition of metric spaces
Takashi Kumagai, Nageswari Shanmugalingam, Ryosuke Shimizu
In the context of a metric measure space , we explore the potential-theoretic implications of having a finite-dimensional Besov space. We prove that if the dimension of th…
Homogeneous Newton-Sobolev spaces in metric measure spaces and their Banach space properties
Nageswari Shanmugalingam
In this note we prove the Banach space properties of the homogeneous Newton-Sobolev spaces of functions on an unbounded metric measure space equipped with a doubl…
Trace and extension theorems for homogeneous Sobolev and Besov spaces for unbounded uniform domains in metric measure spaces
Ryan Gibara, Nageswari Shanmugalingam
In this paper we fix and consider $(\Om,d,μ)$ be an unbounded, locally compact, non-complete metric measure space equipped with a doubling measure supporting a…
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…
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…
Hajlasz Gradients Are Upper Gradients
Renjin Jiang, Nageswari Shanmugalingam, Dachun Yang +1
Let be a metric measure space, with a Borel regular measure. In this paper, we prove that, if and is a Hajłasz gradient…
Geometric analysis on Cantor sets and trees
Anders Björn, Jana Björn, James T. Gill +1
Using uniformization, Cantor type sets can be regarded as boundaries of rooted trees. In this setting, we show that the trace of a first-order Sobolev space on the boundary of a re…
Quasiadditivity of variational capacity
Juha Lehrbäck, Nageswari Shanmugalingam
We study the quasiadditivity property (a version of superadditivity with a multiplicative constant) of variational capacity in metric spaces with respect to Whitney type covers. We…
Equivalence and self-improvement of p-fatness and Hardy's inequality, and association with uniform perfectness
Riikka Korte, Nageswari Shanmugalingam
We present an easy proof that --Hardy's inequality implies uniform --fatness of the boundary when . The proof works also in metric space setting and demonstrates the sel…