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P-harmonic dimensions on ends

Published online by Cambridge University Press:  22 January 2016

Michihiko Kawamura  and
Shigeo Segawa
Michihiko Kawamura
Affiliation:
Department of Mathematics, Faculty of Education, Gifu University, Yanagido, Gifu 501-11, Japan
Shigeo Segawa
Affiliation:
Department of Mathematics, Daido Institute of Technology, Daido, Minami, Nagoya 457, Japan
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Consider an end Ω in the sense of Heins (cf. Heins [3]): Ω is a relatively non-compact subregion of an open Riemann surface such that the relative boundary ∂Ω consists of finitely many analytic Jordan closed curves, there exist no non-constant bounded harmonic functions with vanishing boundary values on ∂Ω and Ω has a single ideal boundary component. A density P = P(z)dxdy (z = x + iy) is a 2-form on Ω∩∂Ω with nonnegative locally Holder continuous coefficient P(z).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 132 , December 1993 , pp. 131 - 139
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1993

References

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