no. 4
On the existence of weighted boundary limits of harmonic functions
Annales de l'Institut Fourier, Volume 40 (1990) no. 4, pp. 811-833

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.

On étudie l’existence de limites tangentielles sur le bord dans un domaine lipschitzien, pour des fonctions harmoniques des classes de Orlicz-Sobolev. L’ensemble exceptionnel est évalué par rapport aux capacités de Bessel et aux mesures de Hausdorff.

Mizuta, Yoshihiro. On the existence of weighted boundary limits of harmonic functions. Annales de l'Institut Fourier, Volume 40 (1990) no. 4, pp. 811-833. doi: 10.5802/aif.1236
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[1] M. Brelot, Élément de la théorie classique du potentiel, 4e édition, Centre de Documentation Universitaire, Paris, 1969.

[2] L. Carleson, Selected problems on exceptional sets, Van Nostrand, Princeton, 1967. | Zbl | MR

[3] A. B. Cruzeiro, Convergence au bord pour les fonctions harmoniques dans Rd de la classe de Sobolev Wd1, C.R.A.S., Paris, 294 (1982), 71-74. | Zbl | MR

[4] N. G. Meyers, A theory of capacities for potentials in Lebesgue classes, Math. Scand., 26 (1970), 255-292. | Zbl | MR

[5] Y. Mizuta, On the Boundary limits of harmonic functions with gradient in Lp, Ann. Inst. Fourier, 34-1 (1984), 99-109. | Zbl | MR | Numdam

[6] Y. Mizuta, On the boundary limits of harmonic functions, Hiroshima Math. J., 18 (1988), 207-217. | Zbl | MR

[7] T. Murai, On the behavior of functions with finite weighted Dirichlet integral near the boundary, Nagoya Math. J., 53 (1974), 83-101. | Zbl | MR

[8] A. Nagel, W. Rudin and J. H. Shapiro, Tangential boundary behavior of functions in Dirichlet-type spaces, Ann. of Math., 116 (1982), 331-360. | Zbl | MR

[9] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, 1970. | Zbl | MR

[10] H. Wallin, on the existence of boundary values of a class of Beppo Levi functions, Trans. Amer. Math. Soc., 120 (1985), 510-525. | Zbl | MR

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