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

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- by Der-Chen Chang, Galia Dafni and Elias M. Stein
- Trans. Amer. Math. Soc.
**351**(1999), 1605-1661 - DOI: https://doi.org/10.1090/S0002-9947-99-02111-X
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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.## References

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## Bibliographic 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
- © Copyright 1999 American Mathematical Society
- 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