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Boundary values of HBD-functions on harmonic boundaries of Riemann surfaces. (English) Zbl 0672.31013

Let R be an open Riemann surface which admits Green functions. The author introduces some new classes of harmonic bounded continuous Dirichlet functions on R. He describes some results on the boundary values of functions in these classes on connected components of the harmonic boundary of R.
Reviewer: W.Okrasinski

MSC:

31C12 Potential theory on Riemannian manifolds and other spaces
30F15 Harmonic functions on Riemann surfaces
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[1] Accola, R: The bilinear relation on open Riemann surfaces. Trans. Amer. Math. Soc, 96, 143-161 (1960). JSTOR: · Zbl 0118.30003
[2] Accola, R: On semi-parabolic Riemann surfaces, ibid., 108, 437-448 (1963). JSTOR: · Zbl 0114.28204
[3] Ahlfors*, L. and Sario, L.: Riemann Surfaces. Princeton Univ. Press (1960). · Zbl 0196.33801
[4] Constantinescu, C. and Cornea, A.: Ideale Rander Riemannscher Flachen. Springer-Verlag (1963). · Zbl 0112.30801
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