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BY 4.0 license Open Access Published by De Gruyter Open Access December 16, 2022

Paatero’s V(k) space II

  • Valentin V. Andreev EMAIL logo , Miron B. Bekker and Joseph A. Cima
From the journal Concrete Operators

Abstract

In this article we continue our investigation of the Paatero space. We prove that the intersection of every Paatero class V(k) with every Hardy space Hp is closed in that Hp and associate singular continuous measures to elements of V(k). There have been no examples in the literature of functions in V(k) with zeros in the unit disk other than the one at the origin. We close this gap in the literature. We derive a representation of the measure associated to a function in V(k) for functions whose derivatives are rational, or algebraic, or transcendental functions in the unit disk.Finally, we consider the notion of regulated domains, introduced by Pommerenke and show that there are regulated domains whose boundary is not of bounded boundary rotation.

MSC 2010: 30C45; 30C15; 30H10

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Received: 2021-12-28
Accepted: 2022-07-21
Published Online: 2022-12-16

© 2022 Valentin V. Andreev et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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