46 citations · 339 across the 63 of their papers we have counts for
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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…
Potential theory and quasisymmetric maps between compact Ahlfors regular metric measure spaces via Besov functions: preliminary
Juha Lehrback, Nageswari Shanmugalingam
We study Besov capacities in a compact Ahlfors regular metric measure space by means of hyperbolic fillings of the space. This approach is applicable even if the space does not sup…
Solving a Dirichlet problem for unbounded domains via a conformal transformation
Ryan Gibara, Riikka Korte, Nageswari Shanmugalingam
In this paper, we solve the -Dirichlet problem for Besov boundary data on unbounded uniform domains with bounded boundaries when the domain is equipped with a doubling measure s…
On Carrasco Piaggio's theorem characterizing quasisymmetric maps from compact doubling spaces to Ahlfors regular spaces
Nageswari Shanmugalingam
In this note we deconstruct and explore the components of a theorem of Carrasco Piaggio, which relates Ahlfors regular conformal gauge of a compact doubling metric space to weights…
Conformal transformation of uniform domains under weights that depend on distance to the boundary
Ryan Gibara, Nageswari Shanmugalingam
The sphericalization procedure converts a Euclidean space into a compact sphere. In this note we propose a variant of this procedure for locally compact, rectifiably path-connected…
Neumann problems for -harmonic functions, and induced nonlocal operators in metric measure spaces
Luca Capogna, Josh Kline, Riikka Korte +2
Following ideas of Caffarelli and Silvestre in~\cite{CS}, and using recent progress in hyperbolic fillings, we define fractional -Laplacians with on any compa…