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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Published electronically: December 18, 2003
MathSciNet review: 2053336
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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: http://dx.doi.org/10.1090/S0002-9939-03-07293-9
PII: S 0002-9939(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