A Luecking-type subspace of $\mathcal {L}^ 1_ a$ and its dual
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- by Pratibha Ghatage and Shun Hua Sun PDF
- Proc. Amer. Math. Soc. 110 (1990), 767-774 Request permission
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.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 110 (1990), 767-774
- MSC: Primary 46E15; Secondary 46B20
- DOI: https://doi.org/10.1090/S0002-9939-1990-1025278-9
- MathSciNet review: 1025278