Denjoy Domains and BMOA
Shengjin Huo, Michel Zinsmeister

TL;DR
This paper proves that for Carleson-homogeneous Denjoy domains, the logarithm of the derivative of their universal covering functions belongs to BMOA, linking geometric domain properties with function space regularity.
Contribution
It establishes a new connection between Carleson-homogeneous Denjoy domains and BMOA regularity of universal coverings, extending previous ideas to a broader class of planar domains.
Findings
If $U$ is a Carleson-homogeneous Denjoy domain, then $ ext{log} {f'} otin BMOA$ for its universal covering.
Develops a general theorem providing sufficient conditions for $ ext{log} {f'} o BMOA$ in planar domains.
Links geometric properties of domains with analytic function space regularity.
Abstract
A Denjoy domain is a plane domain whose complement is a closed subset of the extended real line containing : such a domain is called Carleson-homogeneous if there exists such that for all and , one has , where is the Lebesgue measure on the line. We prove that if is a Carleson-homogeneous Denjoy domain then, if stands for one of its universal coverings, In order to prove this result, we develop ideas from [On Carleson measures induced by Beltrami coefficients being compatible with Fuchsian groups, Ann. Fenn. Math. 46(2021),67-77] leading to a general theorem about planar domains giving sufficient conditions ensuring that for any universal covering
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Meromorphic and Entire Functions · Holomorphic and Operator Theory
