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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Distributions supported in a hypersurface and local $h^p$

Author(s): Galia Dafni
Journal: Proc. Amer. Math. Soc. 126 (1998), 2933-2943.
MSC (1991): Primary 42B30, 46F05
MathSciNet review: 1459116
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Abstract: We give a necessary condition for a distribution with compact support in a hypersurface to be in the local Hardy space ${h^p}({\mathbf{R}^n})$. We apply this condition to prove a result distinguishing two types of Hardy spaces of distributions on a smooth domain $\Omega \subset {\mathbf{R}^n}$.


References:

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D.C. Chang, S. G. Krantz, and E. M. Stein, ${H^p}$ Theory on a smooth domain in $\mathbf{R}^N$ and elliptic boundary value problems, J. Funct. Anal. 114, No. 2 (1993), 286-347. MR 94j:46032
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A. Jonsson, P. Sjögren, and H. Wallin, Hardy and Lipschitz spaces on subsets of ${\mathbf{R}^n}$, Studia Math. 80, No. 2 (1984), 141-166. MR 87b:46022

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Additional Information:

Galia Dafni
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208-2730
Email: dafni@math.nwu.edu

DOI: 10.1090/S0002-9939-98-04437-2
PII: S 0002-9939(98)04437-2
Keywords: $h^p$ spaces, distributions
Received by editor(s): February 28, 1997
Communicated by: Christopher D. Sogge
Copyright of article: Copyright 1998, American Mathematical Society




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