The atomic decomposition in $L^{1}(R^n)$
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- by Wael Abu-Shammala and Alberto Torchinsky PDF
- Proc. Amer. Math. Soc. 135 (2007), 2839-2843 Request permission
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
- W. Abu-Shammala, and A. Torchinsky, Spaces between $H^1(R^n)$ and $L^1(R^n)$, preprint.
- A.-P. Calderón and A. Torchinsky, Parabolic maximal functions associated with a distribution. II, Advances in Math. 24 (1977), no. 2, 101–171. MR 450888, DOI 10.1016/S0001-8708(77)80016-9
- José García-Cuerva and José L. Rubio de Francia, Weighted norm inequalities and related topics, North-Holland Mathematics Studies, vol. 116, North-Holland Publishing Co., Amsterdam, 1985. Notas de Matemática [Mathematical Notes], 104. MR 807149
- Caroline Sweezy, Subspaces of $L^1(\Bbb R^d)$, Proc. Amer. Math. Soc. 132 (2004), no. 12, 3599–3606. MR 2084082, DOI 10.1090/S0002-9939-04-07463-5
- Alberto Torchinsky, Real-variable methods in harmonic analysis, Dover Publications, Inc., Mineola, NY, 2004. Reprint of the 1986 original [Dover, New York; MR0869816]. MR 2059284
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
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 2839-2843
- MSC (2000): Primary 42B25
- DOI: https://doi.org/10.1090/S0002-9939-07-08792-8
- MathSciNet review: 2317960