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

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.

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.

@article{AIF_1990__40_4_811_0,
     author = {Mizuta, Yoshihiro},
     title = {On the existence of weighted boundary limits of harmonic functions},
     journal = {Annales de l'Institut Fourier},
     pages = {811--833},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {40},
     number = {4},
     year = {1990},
     doi = {10.5802/aif.1236},
     zbl = {0715.31002},
     mrnumber = {92g:31010},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1236/}
}
TY  - JOUR
AU  - Mizuta, Yoshihiro
TI  - On the existence of weighted boundary limits of harmonic functions
JO  - Annales de l'Institut Fourier
PY  - 1990
SP  - 811
EP  - 833
VL  - 40
IS  - 4
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1236/
DO  - 10.5802/aif.1236
LA  - en
ID  - AIF_1990__40_4_811_0
ER  - 
%0 Journal Article
%A Mizuta, Yoshihiro
%T On the existence of weighted boundary limits of harmonic functions
%J Annales de l'Institut Fourier
%D 1990
%P 811-833
%V 40
%N 4
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.1236/
%R 10.5802/aif.1236
%G en
%F AIF_1990__40_4_811_0
Mizuta, Yoshihiro. On the existence of weighted boundary limits of harmonic functions. Annales de l'Institut Fourier, Tome 40 (1990) no. 4, pp. 811-833. doi : 10.5802/aif.1236. https://aif.centre-mersenne.org/articles/10.5802/aif.1236/

[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. | MR | Zbl

[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. | MR | Zbl

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

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

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

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

[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. | MR | Zbl

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

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

Cité par Sources :