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On the Bergman number of hyperbolic domains
Dimitrios Betsakos, Nikolaos Karamanlis
We construct a domain in the plane whose Hardy and Bergman numbers satisfy . We also calculate the Bergman number for certain classes of domains having cou…
On the Hardy number and the Bergman number of a planar domain
Dimitrios Betsakos, Francisco J. Cruz-Zamorano
This article deals with functions with a prefixed range and their inclusions in Hardy and weighted Bergman spaces. This idea was originally introduced by Hansen for Hardy spaces, a…
Symmetrization and the rate of convergence of semigroups of holomorphic functions
Dimitrios Betsakos, Argyrios Christodoulou
Let , , be a semigroup of holomorphic self-maps of the unit disk . Let be its Koenigs domain and be its Denjoy-Wolff point…
On the rates of convergence of orbits in semigroups of holomorphic functions
Dimitrios Betsakos, Francisco J. Cruz-Zamorano, Konstantinos Zarvalis
Let be a continuous semigroup of holomorphic self-maps of the unit disk with Denjoy-Wolff point . We study the rate of convergence o…
Semigroups of holomorphic functions; rectifiability and Lipschitz properties of the orbits
Dimitrios Betsakos, Konstantinos Zarvalis
Let be a semigroup of holomorphic functions in the unit disk. We prove that all its orbits are rectifiable and that its forward orbits are Lipschitz curves. Moreover, we fi…
The Hardy number and the Bergman number of a planar domain are equal
Dimitrios Betsakos, Francisco J. Cruz-Zamorano
This article deals with functions with a prefixed range and their inclusion in Hardy and weighted Bergman spaces. This idea was originally introduced by Hansen for Hardy spaces, an…
On the monotonicity of the speeds for semigroups of holomorphic self-maps of the unit disk
Dimitrios Betsakos, Nikolaos Karamanlis
We study semigroups of holomorphic self-maps of the unit disk with Denjoy-Wolff point on the boundary. We show that the orthogonal speed of such semigroups is a s…
Conformal capacity of hedgehogs
Dimitrios Betsakos, Alexander Solynin, Matti Vuorinen
In this paper we discuss problems concerning the conformal condenser capacity of "hedgehogs", which are compact sets in the unit disk consisting of a…