Abstract and Applied Analysis

Multiplicative Isometries on F -Algebras of Holomorphic Functions

Osamu Hatori, Yasuo Iida, Stevo Stević, and Sei-Ichiro Ueki

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Abstract

We study multiplicative isometries on the following F -algebras of holomorphic functions: Smirnov class N * ( X ) , Privalov class N p ( X ) , Bergman-Privalov class A N α p ( X ), and Zygmund F -algebra N log β N ( X ) , where X is the open unit ball 𝔹 n or the open unit polydisk 𝔻 n in n .

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 125987, 16 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1355495629

Digital Object Identifier
doi:10.1155/2012/125987

Mathematical Reviews number (MathSciNet)
MR2872319

Zentralblatt MATH identifier
1236.32002

Citation

Hatori, Osamu; Iida, Yasuo; Stević, Stevo; Ueki, Sei-Ichiro. Multiplicative Isometries on $F$ -Algebras of Holomorphic Functions. Abstr. Appl. Anal. 2012 (2012), Article ID 125987, 16 pages. doi:10.1155/2012/125987. https://projecteuclid.org/euclid.aaa/1355495629


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References

  • O. Hatori and Y. Iida, “Multiplicative isometries on the Smirnov class,” Central European Journal of Mathematics, vol. 9, no. 5, pp. 1051–1056, 2011.
  • S. Stević, “On some isometries on the Bergman-Privalov class on the unit ball,” Nonlinear Analysis, vol. 75, pp. 2448–2454, 2012.
  • K. Stephenson, “Isometries of the Nevanlinna class,” Indiana University Mathematics Journal, vol. 26, no. 2, pp. 307–324, 1977.
  • I. I. Privalov, Boundary Properties of Analytic Functions, Moscow University Press, Moscow, Russia, 1950.
  • I. I. Privalov, Randeigenshaften Analytischer Funktionen, Deutscher Verlag der Wiss., Berlin, Germany, 1956.
  • A. V. Subbotin, “Functional properties of Privalov spaces of holomorphic functions of several vari\
  • A. V. Subbotin, “Isometries of Privalov spaces of holomorphic functions of several variables,” Journal of Mathematical Sciences, vol. 135, no. 1, pp. 2794–2802, 2006.
  • Y. Iida and N. Mochizuki, “Isometries of some F-algebras of holomorphic functions,” Archiv der Mathematik, vol. 71, no. 4, pp. 297–300, 1998.
  • M. Stoll, “Mean growth and Taylor coefficients of some topological algebras of analytic functions,” Annales Polonici Mathematici, vol. 35, no. 2, pp. 139–158, 1978.
  • Y. Matsugu and S. Ueki, “Isometries of weighted Bergman-Privalov spaces on the unit ball of ${\mathbb{C}}^{n}$,” Journal of the Mathematical Society of Japan, vol. 54, no. 2, pp. 341–347, 2002.
  • O. M. Eminyan, “Zygmund \emphF-algebras of holomorphic functions in the ball and in the polydisk,” Doklady Mathematics, vol. 65, no. 3, pp. 353–355, 2002.
  • S. Ueki, “Isometries of the Zygmund \emphF-algebra,” Proceedings of the American Mathematical Society. In press.