This work examines the density of the algebra in H(b) spaces and the boundedness of composition operators in finitely connected domains, suggesting broader implications for function spaces.
In this work, density of the algebra <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:mi mathvariant="script">A</m:mi> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mi>D</m:mi> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> A(D) in H ( b ) spaces of finitely connected planar domains and the boundedness of composition operators on these function spaces are studied. Density of the algebra is considered when the defining function b is a non-extreme point of the unit ball of H ∞ ( D ). In the last part boundedness of composition operators on H ( b ) spaces is considered and as well as a generalization of the unit disk case is given, the boundedness of composition operators with generalized Blaschke symbols over finitely connected domains is characterized.
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Sibel Şahin (2026) studied this question.
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