## Hokkaido Mathematical Journal

### On an $F$-algebra of holomorphic functions on the upper half plane

Yasuo IIDA

#### Abstract

In this paper, we shall consider the class $N^p(D)(p>1)$ of holomorphic functions on the upper half plane $D:=\{ z \in {\bf C} \, | \, \verb|Im| z > 0 \}$ satisfying $\displaystyle \sup_{y>0} \int_{\bf R} \Bigl( \log (1+|f(x+iy)|) \Bigr)^p \,dx < \infty$. We shall prove that $N^p(D)$ is an $F$-algebra with respect to a natural metric on $N^p(D)$. Moreover, a canonical factorization theorem for $N^p(D)$ will be given.

#### Article information

Source
Hokkaido Math. J., Volume 35, Number 3 (2006), 487-495.

Dates
First available in Project Euclid: 29 September 2010

https://projecteuclid.org/euclid.hokmj/1285766413

Digital Object Identifier
doi:10.14492/hokmj/1285766413

Mathematical Reviews number (MathSciNet)
MR2275498

Zentralblatt MATH identifier
1127.30018

#### Citation

IIDA, Yasuo. On an $F$-algebra of holomorphic functions on the upper half plane. Hokkaido Math. J. 35 (2006), no. 3, 487--495. doi:10.14492/hokmj/1285766413. https://projecteuclid.org/euclid.hokmj/1285766413