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

 

The atomic decomposition in $ L^{1}(R^n)$


Authors: Wael Abu-Shammala and Alberto Torchinsky
Journal: Proc. Amer. Math. Soc. 135 (2007), 2839-2843
MSC (2000): Primary 42B25
Published electronically: May 4, 2007
MathSciNet review: 2317960
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Abstract: In this paper we present an atomic decomposition of integrable functions. As an application we compute the distance of $ f$ in $ L^{1}(R^n)$ to the Hardy space $ H^1(R^n)$.


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Additional Information

Wael Abu-Shammala
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: wabusham@indiana.edu

Alberto Torchinsky
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: torchins@indiana.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08792-8
PII: S 0002-9939(07)08792-8
Keywords: Atomic decomposition
Received by editor(s): January 23, 2006
Received by editor(s) in revised form: May 23, 2006
Published electronically: May 4, 2007
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.