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Metric spaces nonembeddable into Banach spaces with the Radon-Nikodým property and thick families of geodesics

Mikhail I. Ostrovskii (2014)

Fundamenta Mathematicae

We show that a geodesic metric space which does not admit bilipschitz embeddings into Banach spaces with the Radon-Nikodým property does not necessarily contain a bilipschitz image of a thick family of geodesics. This is done by showing that no thick family of geodesics is Markov convex, and comparing this result with results of Cheeger-Kleiner, Lee-Naor, and Li. The result contrasts with the earlier result of the author that any Banach space without the Radon-Nikodým property contains a bilipschitz...

Möbius invariant Besov spaces on the unit ball of C n

Małgorzata Michalska, Maria Nowak, Paweł Sobolewski (2011)

Annales UMCS, Mathematica

We give new characterizations of the analytic Besov spaces Bp on the unit ball B of Cn in terms of oscillations and integral means over some Euclidian balls contained in B.

Möbius metric in sector domains

Oona Rainio, Matti Vuorinen (2023)

Czechoslovak Mathematical Journal

The Möbius metric δ G is studied in the cases, where its domain G is an open sector of the complex plane. We introduce upper and lower bounds for this metric in terms of the hyperbolic metric and the angle of the sector, and then use these results to find bounds for the distortion of the Möbius metric under quasiregular mappings defined in sector domains. Furthermore, we numerically study the Möbius metric and its connection to the hyperbolic metric in polygon domains.

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