On a version of Littlewood-Paley function
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P. Szeptycki (1983)
Annales Polonici Mathematici
Fausto Ferrari (1998)
The journal of Fourier analysis and applications [[Elektronische Ressource]]
H. Hueber (1979)
Journal für die reine und angewandte Mathematik
Sadahiro Saeki (1996)
Mathematica Scandinavica
Umberto Neri (1982)
Studia Mathematica
Korenblum, B., Rippon, P.J., Samotij, K. (1995)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
Arsenović, Miloš, Kojić, Vesna, Mateljević, Miodrag (2008)
Annales Academiae Scientiarum Fennicae. Mathematica
Jaroslav Lukes, Jan Maty (1981)
Mathematische Annalen
Yoshihiro Mizuta (1984)
Annales de l'institut Fourier
This paper deals with tangential boundary behaviors of harmonic functions with gradient in Lebesgue classes. Our aim is to extend a recent result of Cruzeiro (C.R.A.S., Paris, 294 (1982), 71–74), concerning tangential boundary limits of harmonic functions with gradient in , denoting the upper half space of the -dimensional euclidean space . Our method used here is different from that of Nagel, Rudin and Shapiro (Ann. of Math., 116 (1982), 331–360); in fact, we use the integral representation...
Paul R. Garabedian (1985)
Revista Matemática Iberoamericana
Over the years many methods have been discovered to prove the existence of a solution of the Dirichlet problem for Laplace's equation. A fairly recent collection of proofs is based on representations of the Green's functions in terms of the Bergman kernel function or some equivalent linear operator [3]. Perhaps the most fundamental of these approaches involves the projection of an arbitrary function onto the class of harmonic functions in a Hilbert space whose norm is defined by the Dirichlet integral...
Yoshihiro Mizuta (1990)
Annales de l'institut Fourier
We study the existence of tangential boundary limits for harmonic functions in a Lipschitz domain, which belong to Orlicz-Sobolev classes. The exceptional sets appearing in this discussion are evaluated by use of Bessel-type capacities as well as Hausdorff measures.
T. Walsh (1971)
Studia Mathematica
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