Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-98-04437-2
MathSciNet review: 1459116
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [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] 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
  • [G] D. Goldberg, A local version of real Hardy spaces, Duke Math. J. 46 (1979), 27-42. MR 80h:46052
  • [H] L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer-Verlag, Berlin 1983. MR 85g:35002a
  • [JSW] 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
  • [M] A. Miyachi, ${H^p}$ spaces over open subsets of ${\mathbf{R}^n}$, Studia Math. 95, No. 3 (1990), 205-228. MR 91m:42022
  • [S] E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, Princeton, New Jersey, 1993. MR 95c:42002

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 42B30, 46F05

Retrieve articles in all journals with MSC (1991): 42B30, 46F05


Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-98-04437-2
Keywords: $h^p$ spaces, distributions
Received by editor(s): February 28, 1997
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society