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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Hilbert spaces of analytic functions between the Hardy and the Dirichlet space


Author: Alexandru Aleman
Journal: Proc. Amer. Math. Soc. 115 (1992), 97-104
MSC: Primary 46E20; Secondary 30D50
MathSciNet review: 1079693
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Abstract: For a large class of Hilbert spaces of analytic functions in the unit disc lying between the Hardy and the Dirichlet space we prove that each element of the space is the quotient of two bounded functions in the same space. It follows that the multiplication operator on these spaces is cellular indecomposable and that each invariant subspace contains nontrivial bounded functions.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1079693-X
PII: S 0002-9939(1992)1079693-X
Article copyright: © Copyright 1992 American Mathematical Society