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International Journal of Analysis
Volume 2017, Article ID 9134768, 4 pages
https://doi.org/10.1155/2017/9134768
Research Article

Bounded Subsets of Smirnov and Privalov Classes on the Upper Half Plane

Department of Mathematics, Kanazawa Medical University, Uchinada, Ishikawa 920-0293, Japan

Correspondence should be addressed to Yasuo Iida; pj.ca.dem-awazanak@adiiy

Received 30 August 2017; Accepted 13 November 2017; Published 19 December 2017

Academic Editor: Ahmed Zayed

Copyright © 2017 Yasuo Iida. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. I. I. Privalov, Boundary Properties of Analytic Functions, Moscow University Press, Moscow, Russia, 1941 (Russian). View at MathSciNet
  2. M. Stoll, “Mean growth and Taylor coefficients of some topological algebras of analytic functions,” Annales Polonici Mathematici, vol. 35, no. 2, pp. 139–158, 1977. View at Publisher · View at Google Scholar · View at MathSciNet
  3. C. M. Eoff, “A representation of as a union of weighted Hardy spaces,” Complex Variables, Theory and Application, vol. 23, no. 3-4, pp. 189–199, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  4. Y. Iida and N. Mochizuki, “Isometries of some F-algebras of holomorphic functions,” Archiv der Mathematik, vol. 71, no. 4, pp. 297–300, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  5. M. Stoll, “The space of holomorphic functions on bounded symmetric domains,” Polska Akademia Nauk. Annales Polonici Mathematici, vol. 32, no. 1, pp. 95–110, 1976. View at Publisher · View at Google Scholar · View at MathSciNet
  6. H. O. Kim, “On an F-algebra of holomorphic functions,” Canadian Journal of Mathematics, vol. 40, no. 3, pp. 718–741, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  7. B. R. Choe and H. O. Kim, “On the boundary behavior of functions holomorphic on the ball,” Complex Variables, Theory and Application, vol. 20, no. 1–4, pp. 53–61, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  8. H. O. Kim and Y. Y. Park, “Maximal functions of plurisubharmonic functions,” Tsukuba Journal of Mathematics, vol. 16, no. 1, pp. 11–18, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  9. V. I. Gavrilov and A. V. Subbotin, “-algebras of holomorphic functions in the ball that contain the Nevanlinna class,” Mathematica Montisnigri, vol. 12, pp. 17–31, 2000 (Russian). View at Google Scholar · View at MathSciNet
  10. N. Mochizuki, “Nevanlinna and Smirnov classes on the upper half plane,” Hokkaido Mathematical Journal, vol. 20, no. 3, pp. 609–620, 1991. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. L. M. Ganzhula, “On an -algebra of holomorphic functions in the upper half-plane,” Mathematica Montisnigri, vol. 12, pp. 33–45, 2000 (Russian). View at Google Scholar · View at MathSciNet
  12. D. A. Efimov and A. V. Subbotin, “Some -algebras of holomorphic functions in the half-plane,” Mathematica Montisnigri, vol. 16, pp. 69–81, 2003 (Russian). View at Google Scholar · View at MathSciNet
  13. Y. Iida, “On an F-algebra of holomorphic functions on the upper half plane,” Hokkaido Mathematical Journal, vol. 35, no. 3, pp. 487–495, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  14. N. Yanagihara, “Bounded subsets of some spaces of holomorphic functions,” Scientific Papers of the College of Arts and Sciences, The University of Tokyo, vol. 23, pp. 19–28, 1973. View at Google Scholar · View at MathSciNet
  15. R. Meštrović, “On -algebras (1 < < ) of holomorphic functions,” The Scientific World Journal, vol. 2014, Article ID 901726, 10 pages, 2014. View at Publisher · View at Google Scholar
  16. D. A. Efimov, “-algebras of holomorphic functions in a half-plane defined by maximal functions,” Doklady Mathematics, vol. 76, no. 2, pp. 755–757, 2007. View at Publisher · View at Google Scholar · View at Scopus
  17. Y. Iida, “Bounded subsets of classes of holomorphic functions,” Journal of Function Spaces, vol. 2017, Article ID 7260602, 4 pages, 2017. View at Publisher · View at Google Scholar · View at MathSciNet