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math.CA2023
Characterization of the upper Assouad codimension
Josh Kline, Antti V. Vähäkangas
We present a new notion, the upper Aikawa codimension, and establish its equivalence with the upper Assouad codimension in a metric space with a doubling measure. To achieve this r…
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…