An approximation property of harmonic functions in Lipschitz domains and some of its consequences
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- by Jorge Rivera-Noriega PDF
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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.References
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Additional Information
- Jorge Rivera-Noriega
- Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
- Email: rnoriega@math.uiuc.edu
- Received by editor(s): February 26, 2002
- Published electronically: December 18, 2003
- Communicated by: Andreas Seeger
- © Copyright 2003 American Mathematical Society
- 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
- MathSciNet review: 2053336