Previous |  Up |  Next

Article

Title: On harmonic majorization of the Martin function at infinity in a cone (English)
Author: Miyamoto, I.
Author: Yanagishita, M.
Author: Yoshida, H.
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 55
Issue: 4
Year: 2005
Pages: 1041-1054
Summary lang: English
.
Category: math
.
Summary: This paper shows that some characterizations of the harmonic majorization of the Martin function for domains having smooth boundaries also hold for cones. (English)
Keyword: harmonic majorization
Keyword: cone
Keyword: minimally thin
MSC: 31B05
MSC: 31B20
idZBL: Zbl 1081.31006
idMR: MR2184382
.
Date available: 2009-09-24T11:30:06Z
Last updated: 2020-07-03
Stable URL: http://hdl.handle.net/10338.dmlcz/128043
.
Reference: [1] H. Aikawa: Sets of determination for harmonic functions in an NTA  domain.J.  Math. Soc. Japan 48 (1996), 299-315. Zbl 0862.31002, MR 1376083, 10.2969/jmsj/04820299
Reference: [2] H.  Aikawa, M.  Essén: Potential Theory-Selected Topics. Lecture Notes in Math. Vol.  1633.Springer-Verlag, , 1996. MR 1439503
Reference: [3] A.  Ancona: Positive Harmonic Functions and Hyperbolicity.Lecture Notes in Math. Vol. 1344, Springer-Verlag, 1987, pp. 1–23. MR 0973878
Reference: [4] D. H. Armitage, Ü. Kuran: On positive harmonic majorization of  $y$ in $\mathbb{R}^{n}\times (0,+\infty )$.J.  London Math. Soc. Ser. II 3 (1971), 733–741. MR 0289799
Reference: [5] D. H. Armitage, S. J. Gardiner: Classical Potential Theory.Springer-Verlag, , 2001. MR 1801253
Reference: [6] V. S.  Azarin: Generalization of a theorem of Hayman on subharmonic functions in an $m$-dimensional cone Am. Math. Soc. Transl. II.  Ser..80 (1969), 119–138.
Reference: [7] A.  Beurling: A minimum principle for positive harmonic functions.Ann. Acad. Sci. Fenn. Ser.  AI. Math. 372 (1965), . Zbl 0139.06402, MR 0188466
Reference: [8] M.  Brelot: On Topologies and Boundaries in Potential Theory. Lect. Notes in Math. Vol.  175.Springer-Verlag, , 1971. MR 0281940
Reference: [9] R.  Courant, D.  Hilbert: Methods of Mathematical Physics, 1st English edition.Interscience, New York, 1954.
Reference: [10] B. E. J.  Dahlberg: A minimum principle for positive harmonic functions.Proc. London Math. Soc. 33 (1976), 2380–250. Zbl 0342.31004, MR 0409847
Reference: [11] J. L.  Doob: Classical Potential Theory and its Probabilistic Counterpart.Springer-Verlag, 1984. Zbl 0549.31001, MR 0731258
Reference: [12] D. S. Jerison, C. E. Kenig: Boundary behavior of harmonic functions in non-tangentially accessible domains.Adv. Math. 46 (1982), 80–147. MR 0676988, 10.1016/0001-8708(82)90055-X
Reference: [13] D.  Gilbarg, N. S.  Trudinger: Elliptic Partial Differential Equations of Second Order.Springer-Verlag, Berlin, 1977. MR 0473443
Reference: [14] L. L.  Helms: Introduction to Potential Theory.Wiley, New York, 1969. Zbl 0188.17203, MR 0261018
Reference: [15] V. G.  Maz’ya: Beurling’s theorem on a minimum principle for positive harmonic functions.Zapiski Nauchnykh Seminarov LOMI 30 (1972). MR 0330484
Reference: [16] I.  Miyamoto, M.  Yanagishitam, and H.  Yoshida: Beurling-Dahlberg-Sjögren type theorems for minimally thin sets in a cone.Canad. Math. Bull. 46 (2003), 252–264. MR 1981679, 10.4153/CMB-2003-025-5
Reference: [17] I.  Miyamoto, H.  Yoshida: Two criteria of Wiener type for minimally thin sets and rarefied sets in a cone.J.  Math. Soc. Japan 54 (2002), 487–512. MR 1900954, 10.2969/jmsj/1191593906
Reference: [18] P.  Sjögren: Une propriété des fonctions harmoniques positives d’après Dahlberg, Séminaire de théorie du potentiel.Lecture Notes in Math. Vol.  563, Springer-Verlag, , 1976, pp. 275–282. MR 0588344
Reference: [19] E. M.  Stein: Singular Integrals and Differentiability Properties of Functions.Princeton University Press, 1970. Zbl 0207.13501, MR 0290095
Reference: [20] H.  Yoshida: Nevanlinna norm of a subharmonic function on a cone or on a cylinder.Proc. London Math. Soc. Ser. III 54 (1987), 267–299. Zbl 0645.31003, MR 0872808
Reference: [21] Y.  Zhang: Ensembles équivalents a un point frontière dans un domaine lipshitzien, Séminaire de théorie du potentiel.Lecture Note in Math. Vol. 1393, Springer-Verlag, , 1989, pp. 256–265. MR 1663163
.

Files

Files Size Format View
CzechMathJ_55-2005-4_18.pdf 382.0Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo