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Paatero’s V(k) space II
- Source :
- Concrete Operators, Vol 9, Iss 1, Pp 151-159 (2022)
- Publication Year :
- 2022
- Publisher :
- De Gruyter, 2022.
-
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.
- Subjects :
- paatero class
hp spaces
geometric function theory
30c45
30c15
30h10
Mathematics
QA1-939
Subjects
Details
- Language :
- English
- ISSN :
- 22993282
- Volume :
- 9
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Concrete Operators
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.38d5811ff08f42e7994e20c57f7f6b59
- Document Type :
- article
- Full Text :
- https://doi.org/10.1515/conop-2022-0134