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On α-Harmonic Functions

Published online by Cambridge University Press:  22 January 2016

Masayuki Itô
Masayuki Itô*
Affiliation:
Mathematical Institute, Nagoya University
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M. Riesz [8] introduced the notion of α-superharmonic functions in n(≥1)-dimensional Euclidean space Rn in connection with the potential of order α. In this paper, we shall first define the α-superharmonic and α-harmonic functions in a domain D. In case α = 2, they coincide with ones in the usual sense.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 26 , February 1966 , pp. 205 - 221
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Brelot, M.: Éléments de la théorie classique du potentiel, Les cours de Sorbonne, 3e cycle, Centre de Documentation Universitaire, Paris, 1960.Google Scholar
[2] Deny, J.: Les potentiels d’énergie finie, Acta Math., 82 (1950), 107–183.Google Scholar
[3] Frostman, O.: Potentiel d’équilibre et capacité des ensembles, Comm. Sem. Math., Lund, 3 (1935), 1–118.Google Scholar
[4] Frostman, O.: Sur les fonctions surharmonique d’ordre fractionnaire, Ark. Math. Astv. Fysik., 16 (1939), 16–35.Google Scholar
[5] Itô, M.: Remarks on Ninomiya’s domination principle, Proc. Jap. Acad., 40 (1964), 743–746.Google Scholar
[6] Ninomiya, N.: Sur un principe du maximum dans la théorie du potentiel, Jour. Math., Osaka City Univ., 12 (1961), 139–143.Google Scholar
[7] Ninomiya, N.: Sur un principe du maximum pour la potentiel du Riesz-Frostman, Jour. Math., Osaka City Univ., 13 (1962), 57–62.Google Scholar
[8] Riesz, M.: Intégrales de Riemann-Liouville et potentiels, Acta Sci. Math., Szeged, 9 (1938), 1–42.Google Scholar
[9] Schwartz, L.: Théorie des distributions 1, Paris Hermann, 1951.Google Scholar