Multiplicative Isometries on F -Algebras of Holomorphic Functions

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 $A{N}_{\alpha }^p(X),$ and Zygmund $F$-algebra $N{\log }^{\beta }N(X),$ where $X$ is the open unit ball ${𝔹}_n$ or the open unit polydisk ${𝔻}^n$ in ${ℂ}^n$.