On the Bergman number of hyperbolic domains

2026/07/15 by Dimitrios Betsakos, Nikolaos Karamanlis
#math.CV

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Abstract

We construct a domain D in the plane whose Hardy and Bergman numbers satisfy 0<h(D)<b(D)<+∞. We also calculate the Bergman number for certain classes of domains having countable complement in the plane. Finally, we investigate some of the implications of our analysis in the theory of iteration of holomorphic self-maps of the unit disk. Our methods rely on estimates for the hyperbolic metric and a recent related result that connects the Bergman number with the hyperbolic metric.

Citations

• The Bergman and the growth numbers of domains and hyperbolic geometry
• Geometric characterizations for conformal mappings in weighted Bergman spaces
• Hyperbolic metric and membership of conformal maps in the Bergman space

Related

• The Bergman number of a plane domain
• The Bergman and the growth numbers of domains and hyperbolic geometry
• The Bergman number of a plane domain
• On the Hardy number and the Bergman number of a planar domain
• On the Hardy number of comb domains