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A Comparison Between thin Sets and Generalized Azarin Sets

Published online by Cambridge University Press:  20 November 2018

M. Essén  and
H. L. Jackson
M. Essén
Affiliation:
Department of Mathematics, Royal Institute of Technology, S-10044 Stockholm 70, Sweden
H. L. Jackson
Affiliation:
Department of Mathematics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
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Let Rp(p≥2) denote p-dimensional Euclidean space, D the half space defined by {P = (x1, x2, …, xp) ∊ Rp: xp > 0} and ∂D the frontier of D in Rp. The Martin boundary (see [2]) of D can be identified with ∂D∪{∞}.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 3 , August 1975 , pp. 335 - 346
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Azarin, V., Generalization of a theorem of Hay man on subharmonic functions in an m-dimensional cone, Amer. Math. Soc. Transi. (2) 80 (1969), 119-138.Google Scholar
2. Brelot, M., On Topologies and Boundaries in Potential Theory, Lecture Notes in Math., 175, Springer, 1971.Google Scholar
3. Carleson, L., Selected problems on exceptional sets, Van Nostrand, 1967.Google Scholar
4. Essén, M. and Lewis, J., The generalized Ahlfors-Heins theorem in certain d-dimensional cones, Proc. of the Conference on Differential Equations in Dundee (March 1972). See Lecture Notes in Mathematics 280, Springer, for general version, and Math. Scand. 33 (1973), 113–129 for detailed version.Google Scholar
5. Jackson, H. L., On minimally thin sets in a Stolzdomain, Can. Math. Bull. 15 (1972), 219-223.Google Scholar
6. Lelong, J., Ètude au voisinage de la frontière des fonctions surharmoniques positives dans un demi-espace, Ann. Sci. École Norm. Sup. (3) 66 (1949), 125-159.Google Scholar
7. Tsuji, M., Potential theory in modem function theory, Maruzen, Tokyo, 1959.Google Scholar
8. Ugaheri, T., On the general potential and capacity Jap. Jour, of Math., 20 (1950), 37-43.Google Scholar