Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces
Volume 2015, Article ID 850709, 6 pages
http://dx.doi.org/10.1155/2015/850709
Research Article

Topological and Functional Properties of Some -Algebras of Holomorphic Functions

Maritime Faculty, University of Montenegro, Dobrota 36, 85330 Kotor, Montenegro

Received 16 June 2015; Accepted 26 August 2015

Academic Editor: Alberto Fiorenza

Copyright © 2015 Romeo Meštrović. 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, Izdat. Moskovskogo Universiteta, Moscow, Russia, 1941.
  2. R. Meštrović and Ž. Pavićević, “Remarks on some classes of holomorphic functions,” Mathematica Montisnigri, vol. 6, pp. 27–37, 1996. View at Google Scholar · View at MathSciNet
  3. N. Mochizuki, “Algebras of holomorphic functions between Hp and N*,” Proceedings of the American Mathematical Society, vol. 105, no. 4, pp. 898–902, 1989. View at Google Scholar
  4. C. M. Eoff, “A representation of Nα+ 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
  5. 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 Google Scholar · View at MathSciNet
  6. R. Meštrović, Topological and F-algebras of holomorphic functions [Ph.D. thesis], University of Montenegro, Podgorica, Montenegro, 1999.
  7. R. Meštrović and Ž. Pavićević, “Topologies on some subclasses of the Smirnov class,” Acta Scientiarum Mathematicarum, vol. 69, no. 1-2, pp. 99–108, 2003. View at Google Scholar · View at MathSciNet
  8. 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 · View at Scopus
  9. Y. Matsugu, “Invariant subspaces of the Privalov spaces,” Far East Journal of Mathematical Sciences, vol. 2, no. 4, pp. 633–643, 2000. View at Google Scholar · View at MathSciNet
  10. R. Meštrović and Ž. Pavićević, “Weakly dense ideals in Privalov spaces of holomorphic functions,” Journal of the Korean Mathematical Society, vol. 48, no. 2, pp. 397–420, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. R. Meštrović, “Maximal ideals in some F-algebras of holomorphic functions,” Filomat, vol. 29, no. 1, pp. 1–5, 2015. View at Publisher · View at Google Scholar
  12. R. Meštrović and J. Šušić, “Interpolation in the spaces Np(1<p<),” Filomat, vol. 27, no. 2, pp. 291–299, 2013. View at Google Scholar
  13. N. Yanagihara, “Multipliers and linear functionals for the class N+,” Transactions of the American Mathematical Society, vol. 180, pp. 449–461, 1973. View at Google Scholar · View at MathSciNet
  14. R. Meštrović, “On F-algebras Mp(1<p<) of holomorphic functions,” The Scientific World Journal, vol. 2014, Article ID 901726, 10 pages, 2014. View at Publisher · View at Google Scholar
  15. C. M. Eoff, “Fréchet envelopes of certain algebras of analytic functions,” The Michigan Mathematical Journal, vol. 35, no. 3, pp. 413–426, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  16. R. Meštrović, “The failure of the Hahn-Banach properties in Privalov spaces of holomorphic functions,” Mathematica Montisnigri, vol. 17, pp. 27–36, 2004. View at Google Scholar · View at MathSciNet
  17. R. Meštrović and Ž. Pavićević, “A topological property of Privalov spaces on the unit disk,” Mathematica Montisnigri, vol. 31, pp. 5–15, 2014. View at Google Scholar
  18. N. Yanagihara, “The containing Fréchet space for the class N+,” Duke Mathematical Journal, vol. 40, no. 1, pp. 93–103, 1973. View at Publisher · View at Google Scholar · View at MathSciNet
  19. J. H. Shapiro, “Mackey topologies, reproducing kernels, and diagonal maps on the Hardy and Bergman spaces,” Duke Mathematical Journal, vol. 43, no. 1, pp. 187–202, 1976. View at Publisher · View at Google Scholar · View at MathSciNet
  20. J. E. Kelley and I. Namioka, Linear Topological Spaces, Princeton, 1963.
  21. R. Meštrović and A. V. Subbotin, “Multipliers and linear functionals for Privalov spaces of holomorphic functions in the disc,” Doklady Akademii Nauk, vol. 365, no. 4, pp. 452–454, 1999 (Russian). View at Google Scholar
  22. J. E. McCarthy, “Common range of co-analytic Toeplitz operators,” Journal of the American Mathematical Society, vol. 3, no. 4, pp. 793–799, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  23. W. Rudin, Functional Analysis, McGraw-Hill, New York, NY, USA, 1973. View at MathSciNet
  24. G. Köthe, Topological Vector Spaces I, Springer, Heidelberg, Germany, 1969. View at MathSciNet
  25. N. Yanagihara, “The second dual space for the space N+,” Proceedings of the Japan Academy, vol. 49, no. 1, pp. 33–36, 1973. View at Publisher · View at Google Scholar