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Subspaces of $L^{1}(\mathbb{R} ^{d})$

Author: Caroline Sweezy
Journal: Proc. Amer. Math. Soc. 132 (2004), 3599-3606
MSC (2000): Primary 42B25
Published electronically: July 12, 2004
MathSciNet review: 2084082
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Abstract: The relationship of the Hardy space $H^{1}(R^{d})$ and the space of integrable functions $L^{1}(R^{d})$ is examined in terms of intermediate spaces of functions that are described as sums of atoms. It is proved that these spaces have dual spaces that lie between the space of functions of bounded mean oscillation, $BMO$, and $L^{\infty }$. Furthermore, the spaces intermediate to $H^{1}$ and $L^{1}$ are shown to be dual to spaces similar to the space of functions of vanishing mean oscillation. The proofs are extensions of classical proofs.

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Additional Information

Caroline Sweezy
Affiliation: Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003

Received by editor(s): June 23, 2003
Published electronically: July 12, 2004
Communicated by: Andreas Seeger
Article copyright: © Copyright 2004 American Mathematical Society