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

A Luecking-type subspace of $ \mathcal{L}\sp 1\sb a$ and its dual


Authors: Pratibha Ghatage and Shun Hua Sun
Journal: Proc. Amer. Math. Soc. 110 (1990), 767-774
MSC: Primary 46E15; Secondary 46B20
MathSciNet review: 1025278
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Abstract: The purpose of this investigation is to determine the extent to which Luecking's decomposition of Bergman spaces $ \mathcal{L}_a^p,(1 < p < \infty )$ [4] can be extended to $ \mathcal{L}_a^1$. The set of functions for which an atomic decomposition (using the reproducing kernel of the Bergman space) is possible turns out to be only a small part of $ \mathcal{L}_a^1$. In this note we equip each of such functions with a new norm and study the resulting Banach space. We describe its dual and predual.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1025278-9
PII: S 0002-9939(1990)1025278-9
Article copyright: © Copyright 1990 American Mathematical Society