The Range of Hardy Numbers for Comb Domains

Karafyllia, Christina

doi:10.1007/s40315-021-00426-0

Comput. Methods Funct. Theory

2021

DOI: 10.1007/s40315-021-00426-0

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The Range of Hardy Numbers for Comb Domains

Christina Karafyllia

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2024

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Cited by 2 publications

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On the Hardy number of Koenigs domains

Contreras,

Cruz-Zamorano,

Kourou

et al. 2024

Anal.Math.Phys.

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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.

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On the Hardy number of Koenigs domains

Contreras,

Cruz-Zamorano,

Kourou

et al. 2024

Anal.Math.Phys.

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A Collection of Results Relating the Geometry of Plane Domains and the Exit Time of Planar Brownian Motion

Boudabra

Buttigieg

Markowsky

2022

Comput. Methods Funct. Theory

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We prove a number of results relating exit times of planar Brownian motion with the geometric properties of the domains in question. Included are proofs of the conformal invariance of moduli of rectangles and annuli using Brownian motion; similarly probabilistic proofs of some recent results of Karafyllia on harmonic measure on starlike domains; examples of domains and their complements which are simultaneously large when measured by the moments of exit time of Brownian motion, and examples of domains and their complements which are simultaneously small; and proofs of several identities involving the Cauchy distribution using the optional stopping theorem.

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The Range of Hardy Numbers for Comb Domains

Cited by 2 publications

References 8 publications

On the Hardy number of Koenigs domains

On the Hardy number of Koenigs domains

A Collection of Results Relating the Geometry of Plane Domains and the Exit Time of Planar Brownian Motion

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