On an $F$-algebra of holomorphic functions on the upper half plane
IIDA, Yasuo
Hokkaido Math. J., Tome 35 (2006) no. 1, p. 487-495 / Harvested from Project Euclid
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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.
Publié le : 2006-08-15
Classification:  Nevanlinna-type spaces,  Nevanlinna class,  Smirnov class,  $N^p$,  Hardy spaces,  46E10,  30H05 
@article{1285766413,
     author = {IIDA, Yasuo},
     title = {On an $F$-algebra of holomorphic functions on the upper half plane},
     journal = {Hokkaido Math. J.},
     volume = {35},
     number = {1},
     year = {2006},
     pages = { 487-495},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1285766413}
}

IIDA, Yasuo. On an $F$-algebra of holomorphic functions on the upper half plane. Hokkaido Math. J., Tome 35 (2006) no. 1, pp.  487-495. http://gdmltest.u-ga.fr/item/1285766413/