Work

On the Hardy number of Koenigs domains

Year: 2024

Type: article

Abstract: This work studies the Hardy number of hyperbolic planar domains satisfying Abel’s inclusion property, which are usually known as Koenigs domains. More explicitly, we prove that the Hardy number of a Koenings domains whose complement is non-polar is greater than or equal to 1/2, and this lower bound is sharp. In contrast to this result, we provide examples of general domains whose Hardy numbers are arbitrarily small. Additionally, we outline the connection of the aforementioned class of domains with the discrete dynamics of the unit disc and obtain results on the range of Hardy number of Koenigs maps, in the hyperbolic and parabolic case.

Source: Analysis and Mathematical Physics

DOI: 10.1007/s13324-024-00981-4

Authors: Manuel D. Contreras, Francisco J. Cruz-Zamorano, Maria Kourou, Luis Rodríguez-Piazza

Institutions: Universidad de Sevilla, University of Würzburg

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Alexander von Humboldt-Stiftung, Universidad de Sevilla, Junta de Andalucía