An approximation property of harmonic functions in Lipschitz domains and some of its consequences

Author:
Jorge Rivera-Noriega

Translated by:

Journal:
Proc. Amer. Math. Soc. **132** (2004), 1321-1331

MSC (2000):
Primary 42B25, 35J67

DOI:
https://doi.org/10.1090/S0002-9939-03-07293-9

Published electronically:
December 18, 2003

MathSciNet review:
2053336

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Abstract | References | Similar Articles | Additional Information

Abstract: An extension of an inequality of J. B. Garnett (1979), with improvements by B. E. J. Dahlberg (1980), on an approximation property of harmonic functions is proved. The weighted inequality proved here was suggested by the work of J. Pipher (1993) and it implies an extension of a result of S. Y. A. Chang, J. Wilson and T. Wolff (1985) and C. Sweezy (1991) on exponential square integrability of the boundary values of solutions to second-order linear differential equations in divergence form. This implies a solution of a problem left open by R. Bañuelos and C. N. Moore (1989) on sharp estimates for the area integral of harmonic functions in Lipschitz domains.

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Additional Information

**Jorge Rivera-Noriega**

Affiliation:
Department of Mathematics, University of Illinois, Urbana, Illinois 61801

Email:
rnoriega@math.uiuc.edu

DOI:
https://doi.org/10.1090/S0002-9939-03-07293-9

Keywords:
Approximation of harmonic functions,
exponential square class,
area integral estimates

Received by editor(s):
February 26, 2002

Published electronically:
December 18, 2003

Communicated by:
Andreas Seeger

Article copyright:
© Copyright 2003
American Mathematical Society