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Proceedings of the American Mathematical Society

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

Author: 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 $\Omega \subset {\mathbf{R}^n}$.

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  • [CDS] D.C. Chang, G. Dafni, and E. M. Stein, Hardy spaces, BMO, and boundary value problems for the Laplacian on a smooth domain in ${\mathbf{R}^n}$, Trans. Amer. Math. Soc., to appear. CMP 97:15
  • [CKS] Der-Chen Chang, Steven G. Krantz, and Elias M. Stein, 𝐻^{𝑝} theory on a smooth domain in 𝑅^{𝑁} and elliptic boundary value problems, J. Funct. Anal. 114 (1993), no. 2, 286–347. MR 1223705, 10.1006/jfan.1993.1069
  • [G] David Goldberg, A local version of real Hardy spaces, Duke Math. J. 46 (1979), no. 1, 27–42. MR 523600
  • [H] Lars Hörmander, The analysis of linear partial differential operators. I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 256, Springer-Verlag, Berlin, 1983. Distribution theory and Fourier analysis. MR 717035
  • [JSW] Alf Jonsson, Peter Sjögren, and Hans Wallin, Hardy and Lipschitz spaces on subsets of 𝑅ⁿ, Studia Math. 80 (1984), no. 2, 141–166. MR 781332
  • [M] Akihiko Miyachi, 𝐻^{𝑝} spaces over open subsets of 𝑅ⁿ, Studia Math. 95 (1990), no. 3, 205–228. MR 1060724
  • [S] Elias M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993. With the assistance of Timothy S. Murphy; Monographs in Harmonic Analysis, III. MR 1232192

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Additional Information

Galia Dafni
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208-2730

Keywords: $h^p$ spaces, distributions
Received by editor(s): February 28, 1997
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1998 American Mathematical Society