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Characterization of John domains via weak tangents
Christina Karafyllia
We characterize simply connected John domains in the plane with the aid of weak tangents of the boundary. Specifically, we prove that a bounded simply connected domain is a Joh…
Unbounded Hölder domains
Christina Karafyllia
Motivated by the classical bounded Hölder domains, we introduce the notion of an unbounded simply connected Hölder domain. We prove analytic and geometric characterizations of thos…
Uniformization of Gromov hyperbolic domains by circle domains
Christina Karafyllia, Dimitrios Ntalampekos
We prove that a domain in the Riemann sphere is Gromov hyperbolic if and only if it is conformally equivalent to a uniform circle domain. This resolves a conjecture of Bonk--Heinon…
Extremal distance and conformal mappings in Hardy and Bergman spaces
Christina Karafyllia
We prove necessary and sufficient integral conditions involving extremal distance for a conformal mapping of the unit disk to belong to the Hardy or weighted Bergman spaces. We als…
Geometric characterizations for conformal mappings in weighted Bergman spaces
Christina Karafyllia, Nikolaos Karamanlis
We prove that a conformal mapping defined on the unit disk belongs to a weighted Bergman space if and only if certain integrals involving the harmonic measure converge. With the ai…
The range of Hardy number on comb domains
Christina Karafyllia
Let be a simply connected domain and be the Riemann mapping from onto . The Hardy number of is the supremum of all for which belon…