Contreras Márquez, Manuel DomingoCruz Zamorano, Francisco JoséKourou, MaríaRodríguez Piazza, Luis2025-01-232025-01-232024-12Contreras, Manuel D., Cruz-Zamorano, Francisco .J., Kourou, M. y Rodríguez-Piazza, L. (2024). On the Hardy number of Koenigs domains. Analysis and Mathematical Physics, 14 (6), 119. https://doi.org/10.1007/s13324-024-00981-4.1664-23681664-235Xhttps://hdl.handle.net/11441/167370Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.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.application/pdf21 p.engAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/Hardy spacesAbel’s equationKoenigs domainIteration in the unit discKoenigs mapinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1007/s13324-024-00981-4