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 | References | Similar Articles | Additional Information

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

MR Author ID:
47325

Email:
drc@math.umd.edu

**Galia Dafni**

Affiliation:
Department of Mathematics & Statistics, Concordia University, Montreal, Quebec H3G-1M8, Canada

MR Author ID:
255789

ORCID:
0000-0002-5078-7724

Email:
gdafni@discrete.concordia.ca

**Elias M. Stein**

Affiliation:
Department of Mathematics, Princeton University, Princeton, New Jersey 08544

MR Author ID:
166825

Email:
stein@math.princeton.edu

Received by editor(s):
September 5, 1996

Received by editor(s) in revised form:
March 20, 1997

Article copyright:
© Copyright 1999
American Mathematical Society