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

Author(s): Wael Abu-Shammala; Alberto Torchinsky
Journal: Proc. Amer. Math. Soc. 135 (2007), 2839-2843.
MSC (2000): Primary 42B25
Posted: May 4, 2007
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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)$.

References:

1.
W. Abu-Shammala, and A. Torchinsky, Spaces between $ H^1(R^n)$ and $ L^1(R^n)$, preprint.

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A. P. Calderón and A. Torchinsky, Parabolic maximal functions associated with a distribution, II, Advances in Math., 24 (1977), 101-171. MR 0450888 (56:9180)

3.
J. García-Cuerva and J. L. Rubio de Francia, Weighted norm inequalities and related topics, Notas de Matemática 116, North Holland, 1985. MR 0807149 (87d:42023)

4.
C. Sweezy, Subspaces of $ L^1(R^d)$, Proc. Amer. Math. Soc. 132 (2005), 3599-3606. MR 2084082 (2005h:42053)

5.
A. Torchinsky, Real-variable methods in harmonic analysis, Dover Publications, Inc., 2004.MR 2059284

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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: 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
Posted: May 4, 2007
Communicated by: Michael T. Lacey
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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