Dirichlet problem in Lipschitz domains with BMO data

Fabes, Eugene B.; Neri, Umberto

doi:10.1090/S0002-9939-1980-0548079-8

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

Björn E. J. Dahlberg, Estimates of harmonic measure, Arch. Rational Mech. Anal. 65 (1977), no. 3, 275–288. MR 466593, DOI 10.1007/BF00280445

On the Poisson integral for Lipschitz and

domains

Weighted norm inequalities for the Lusin area integral and the nontangential maximal function for functions harmonic in a Lipschitz domain

estimates for Green potentials in Lipschitz domains

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. 2, 159–170. MR 394172, DOI 10.1512/iumj.1976.25.25012

Harmonic functions with BMO traces Lipschitz curves

Richard A. Hunt and Richard L. Wheeden, On the boundary values of harmonic functions, Trans. Amer. Math. Soc. 132 (1968), 307–322. 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. 3, 221–237. MR 399741, DOI 10.4064/sm-54-3-221-237