Ishida, Hisashi Boundary values of HBD-functions on harmonic boundaries of Riemann surfaces. (English) Zbl 0672.31013 Proc. Japan Acad., Ser. A 64, No. 6, 181-183 (1988). 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 Keywords:Riemann surface; Green functions; harmonic; Dirichlet functions; boundary values PDFBibTeX XMLCite \textit{H. Ishida}, Proc. Japan Acad., Ser. A 64, No. 6, 181--183 (1988; Zbl 0672.31013) Full Text: DOI References: [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 [5] Ishida, H.: Harmonic Dirichlet functions and the components of harmonic boundaries of Riemann surfaces (to appear). · Zbl 0721.30030 [6] Kusunoki, Y.: Characterizations of canonical differentials. J. Math. Kyoto Univ., 5,197-207 (1966). · Zbl 0156.09001 [7] Kusunoki, Y. and Mori, S.: Some remarks on boundary values of harmonic functions with finite Dirichlet integrals, ibid., 7, 315-324 (1968). · Zbl 0159.16001 [8] Sario, L. and Nakai, M.: Classification Theory of Riemann Surfaces. Springer-Verlag (1970). · Zbl 0199.40603 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.