Beurling-Dahlberg-Sjögren Type Theorems for Minimally Thin Sets in a Cone
Canadian mathematical bulletin, Tome 46 (2003) no. 2, pp. 252-264

Voir la notice de l'article provenant de la source Cambridge University Press

This paper shows that some characterizations of minimally thin sets connected with a domain having smooth boundary and a half-space in particular also hold for the minimally thin sets at a corner point of a special domain with corners, i.e., the minimally thin set at $\infty$ of a cone.
DOI : 10.4153/CMB-2003-025-5
Mots-clés : 31B05, 31B20
Miyamoto, Ikuko; Yanagishita, Minoru; Yoshida, Hidenobu. Beurling-Dahlberg-Sjögren Type Theorems for Minimally Thin Sets in a Cone. Canadian mathematical bulletin, Tome 46 (2003) no. 2, pp. 252-264. doi: 10.4153/CMB-2003-025-5
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[1] [1] Aikawa, H., Quasiadditivity of Riesz capacity. Math. Scand. 69 (1991), 15–30. Google Scholar

[2] [2] Aikawa, H., Quasiadditivity of capacity and minimal thinness. Ann. Acad. Sci. Fenn.Math. Ser. AI 18 (1993), 65–75. Google Scholar

[3] [3] Aikawa, H. and Essén, M., Potential Theory-Selected Topics. Lecture Notes in Math. 1633, Springer-Verlag, 1996. Google Scholar

[4] [4] Ancona, A., On strong barriers and an inequality of Hardy for domains in Rn. J. LondonMath. Soc. (2) 34 (1986), 274–290. Google Scholar

[5] [5] Azarin, V. S., Generalization of a theorem of Hayman on subharmonic functions in an m-dimensional cone. Mat. Sb. 66 (108)(1965), 248–264; Amer.Math. Soc. Transl. (2) 80 (1969), 119–138. Google Scholar

[6] [6] Beurling, A., A minimum principle for positive harmonic functions. Ann. Acad. Sci. Fenn. Ser. AI. Math. 372, 1965. Google Scholar

[7] [7] Brelot, M., On topologies and boundaries in potential theory. Lecture Notes in Math. 175, Springer-Verlag, 1971. Google Scholar

[8] [8] Courant, R. and Hilbert, D., Methods of mathematical physics. 1st English edition, Interscience, New York, 1954. Google Scholar

[9] [9] Dahlberg, B. E. J., A minimum principle for positive harmonic functions. Proc. London Math. Soc. (3) 33 (1976), 238–250. Google Scholar

[10] [10] Doob, J. I., Classical potential theory and its probabilistic counterpart. Springer-Verlag, 1984. Google Scholar

[11] [11] Essén, M. and Jackson, H. L., On the covering properties of certain exceptional sets in a half-space. Hiroshima Math. J. 10 (1980), 233–262. Google Scholar

[12] [12] Gilbarg, D. and Trudinger, N. S., Elliptic partial differential equations of second order. Springer-Verlag, Berlin, 1977. Google Scholar

[13] [13] Helms, L. L., Introduction to potential theory. Wiley, New York, 1969. Google Scholar

[14] [14] Lewis, J. L., Uniformly fat sets. Trans. Amer.Math. Soc. 308 (1988), 177–196. Google Scholar

[15] [15] Miyamoto, I. and Yoshida, H., Two criteria of Wiener type for minimally thin sets and rareèd sets in a cone. J. Math. Soc. Japan, to appear. Google Scholar

[16] [16] Sjögren, P., Une propriété des fonctions harmoniques positives d'après Dahlberg. In: Séminaire de théorie du potentiel, Lecture Notes in Math. 563, Springer, Berlin, 1976, 275–282. Google Scholar

[17] [17] Stein, E. M., Singular integrals and differentiability properties of functions. Princeton University Press, 1970. Google Scholar

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