In this paper we give characterizations of those holomorphic functions in the unit disc in the complex plane that can be written as a quotient of functions in A(D), A∞(D) or Λ1(D) with a nonvanishing denominator in D. As a consequence we prove that if f ∈ Λ1(D) does not vanish in D, then there exists g ∈ Λ1(D) which has the same zero set as f in Dbar and such that fg ∈ A∞(D).
@article{urn:eudml:doc:41031,
title = {On quotients of holomorphic funtions in the dics with boundary regularity conditions.},
journal = {Publicacions Matem\`atiques},
volume = {32},
year = {1988},
pages = {135-144},
mrnumber = {MR0939778},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41031}
}
Ortega, Joaquín M. On quotients of holomorphic funtions in the dics with boundary regularity conditions.. Publicacions Matemàtiques, Tome 32 (1988) pp. 135-144. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41031/