Dirichlet problem in Lipschitz domains with BMO data
HTML articles powered by AMS MathViewer
- by Eugene B. Fabes and Umberto Neri PDF
- Proc. Amer. Math. Soc. 78 (1980), 33-39 Request permission
Abstract:
In any bounded starlike Lipschitz domain, the harmonic functions whose boundary values are in BMO (the class of functions with bounded mean oscillation) of the boundary are shown to be characterized by the property that their Littlewood-Paley measures are Carleson measures. This result extends the analogous characterization found by the authors when the domain in question is a half-space.References
- Bjรถrn E. J. Dahlberg, Estimates of harmonic measure, Arch. Rational Mech. Anal. 65 (1977), no.ย 3, 275โ288. MR 466593, DOI 10.1007/BF00280445 โ, On the Poisson integral for Lipschitz and ${C^1}$ domains, Studia Math. (to appear) โ, Weighted norm inequalities for the Lusin area integral and the nontangential maximal function for functions harmonic in a Lipschitz domain, Chalmers Inst. Technology and Univ. of Goteborg, 1977 (preprint). โ, ${L^q}$ estimates for Green potentials in Lipschitz domains Tech. Rep., Chalmers Inst. Technology and Univ. of Goteborg, 1977.
- E. B. Fabes, R. L. Johnson, and U. Neri, Spaces of harmonic functions representable by Poisson integrals of functions in $\textrm {BMO}$ and ${\cal L}_{p,\lambda }$, Indiana Univ. Math. J. 25 (1976), no.ย 2, 159โ170. MR 394172, DOI 10.1512/iumj.1976.25.25012 E. Fabes and U. Neri, Harmonic functions with BMO traces Lipschitz curves, Tech. Rep. 78-41, University of Maryland, July, 1978.
- Richard A. Hunt and Richard L. Wheeden, On the boundary values of harmonic functions, Trans. Amer. Math. Soc. 132 (1968), 307โ322. MR 226044, DOI 10.1090/S0002-9947-1968-0226044-7
- Benjamin Muckenhoupt and Richard L. Wheeden, Weighted bounded mean oscillation and the Hilbert transform, Studia Math. 54 (1975/76), no.ย 3, 221โ237. MR 399741, DOI 10.4064/sm-54-3-221-237
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 78 (1980), 33-39
- MSC: Primary 31B05; Secondary 31B25
- DOI: https://doi.org/10.1090/S0002-9939-1980-0548079-8
- MathSciNet review: 548079