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Hardy spaces, BMO, and boundary value problems for the Laplacian on a smooth domain in $\mathbf{R}^n$


Authors: Der-Chen Chang, Galia Dafni and Elias M. Stein
Journal: Trans. Amer. Math. Soc. 351 (1999), 1605-1661
MSC (1991): Primary 35J25, 42B25; Secondary 46E15, 42B30
DOI: https://doi.org/10.1090/S0002-9947-99-02111-X
MathSciNet review: 1458319
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Abstract: We study two different local $H^p$ spaces, $0 < p \leq 1$, on a smooth domain in $\mathbf{R}^n$, by means of maximal functions and atomic decomposition. We prove the regularity in these spaces, as well as in the corresponding dual BMO spaces, of the Dirichlet and Neumann problems for the Laplacian.


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Additional Information

Der-Chen Chang
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Address at time of publication: Department of Mathematics, Georgetown University, Washingon, DC 20057
Email: drc@math.umd.edu

Galia Dafni
Affiliation: Department of Mathematics & Statistics, Concordia University, Montreal, Quebec H3G-1M8, Canada
Email: gdafni@discrete.concordia.ca

Elias M. Stein
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544
Email: stein@math.princeton.edu

DOI: https://doi.org/10.1090/S0002-9947-99-02111-X
Received by editor(s): September 5, 1996
Received by editor(s) in revised form: March 20, 1997
Article copyright: © Copyright 1999 American Mathematical Society

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