Abstract and Applied Analysis
Volume 2012 (2012), Article ID 125987, 16 pages
http://dx.doi.org/10.1155/2012/125987
Research Article

Multiplicative Isometries on 𝐹 -Algebras of Holomorphic Functions

Osamu Hatori,1 Yasuo Iida,2 Stevo Stević,3 and Sei-Ichiro Ueki4

1Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-2181, Japan
2Department of Mathematics, Iwate Medical University, Yahaba, Iwate 028-3694, Japan
3Mathematical Institute of the Serbian Academy of Sciences, Knez Mihailova 36/III, 11000 Beograd, Serbia
4Faculty of Engineering, Ibaraki University, Hitachi 316-8511, Japan

Received 12 July 2011; Accepted 11 October 2011

Academic Editor: Norio Yoshida

Copyright © 2012 Osamu Hatori et al. 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.

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 𝑝 𝛼 ( 𝑋 ) , and Zygmund 𝐹 -algebra 𝑁 l o g 𝛽 𝑁 ( 𝑋 ) , where 𝑋 is the open unit ball 𝔹 𝑛 or the open unit polydisk 𝔻 𝑛 in ℂ 𝑛 .