43 citations · 420 across the 43 of their papers we have counts for
8 papers · 1 filter
Sharp Besov capacity estimates for annuli in metric spaces with doubling measures
Anders Björn, Jana Björn
We obtain precise estimates, in terms of the measure of balls, for the Besov capacity of annuli and singletons in complete metric spaces. The spaces are only assumed to be uniforml…
Poincaré inequalities and weights on bow-ties
Anders Björn, Jana Björn, Andreas Christensen
A metric space is called a \emph{bow-tie} if it can be written as , where and are closed subsets of . We…
Classification of metric measure spaces and their ends using -harmonic functions
Anders Bjorn, Jana Bjorn, Nageswari Shanmugalingam
By seeing whether a Liouville type theorem holds for positive, bounded, and/or finite energy -harmonic and -quasiharmonic functions, we classify proper metric spaces equipped…
Extension and trace results for doubling metric measure spaces and their hyperbolic fillings
Anders Bjorn, Jana Bjorn, Nageswari Shanmugalingam
In this paper we study connections between Besov spaces of functions on a compact metric space , equipped with a doubling measure, and the Newton--Sobolev space of functions on…
Bounded geometry and -harmonic functions under uniformization and hyperbolization
Anders Bjorn, Jana Bjorn, Nageswari Shanmugalingam
The uniformization and hyperbolization transformations formulated by Bonk, Heinonen and Koskela in \emph{"Uniformizing Gromov Hyperbolic Spaces"}, Astérisque {\bf 270} (2001), deal…
The Mazurkiewicz distance and sets that are finitely connected at the boundary
Anders Björn, Jana Björn, Nageswari Shanmugalingam
We study local connectedness, local accessibility and finite connectedness at the boundary, in relation to the compactness of the Mazurkiewicz completion of a bounded domain in a m…
The Dirichlet problem for p-harmonic functions with respect to the Mazurkiewicz boundary
Anders Bjorn, Jana Bjorn, Nageswari Shanmugalingam
In this paper we develop the Perron method for solving the Dirichlet problem for the analog of the p-Laplacian, i.e. for p-harmonic functions, with Mazurkiewicz boundary values. Th…
Prime ends for domains in metric spaces
Tomasz Adamowicz, Anders Bjorn, Jana Bjorn +1
In this paper we propose a new definition of prime ends for domains in metric spaces under rather general assumptions. We compare our prime ends to those of Carathéodory and Näkki.…