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math.FA2026
Sobolev extensions, interpolation inequalities and consequences
Rupert L. Frank, Pekka Koskela, Riddhi Mishra
We prove Sobolev interpolation inequalities on extension domains that have a form reminiscent of the corresponding whole-space inequalities. This form is crucial in certain applica…
math.FA2026
Exceptional Sets for Quasiconformal Mappings in General Metric Spaces II
Behnam Esmayli, Pekka Koskela, Khanh Nguyen
A homemorphism between domains in , is quasiconformal, with its intricate analytic and geometric consequences, if the (pointwise) linear dilatation -- a purel…
math.FA2023
Large-scale behaviour of Sobolev functions in Ahlfors regular metric measure spaces
Josh Kline, Pekka Koskela, Khanh Nguyen
In this paper, we study the behaviour at infinity of -Sobolev functions in the setting of Ahlfors -regular metric measure spaces supporting a -Poincaré inequality. By intr…