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Proceedings of the American Mathematical Society

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Spaces between $ H^{1}$ and $ L^{1}$


Authors: Wael Abu-Shammala and Alberto Torchinsky
Journal: Proc. Amer. Math. Soc. 136 (2008), 1743-1748
MSC (2000): Primary 42B25
DOI: https://doi.org/10.1090/S0002-9939-08-09223-X
Published electronically: January 25, 2008
MathSciNet review: 2373604
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Abstract: In this paper we consider the spaces $ X_s$ that lie between $ H^1(R^n)$ and $ L^1(R^n)$. We discuss their interpolation properties and the behavior of maximal functions and singular integrals acting on them.


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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: https://doi.org/10.1090/S0002-9939-08-09223-X
Keywords: $K$ functional
Received by editor(s): March 19, 2007
Published electronically: January 25, 2008
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2008 American Mathematical Society