International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 4, Pages 785-789
doi:10.1155/S0161171286000959
On a generalization of the corona problem
Scuola Normale Superiore, Piazza dei Cavalieri, 7, Pisa 56100 , Italy
Received 7 May 1985
Copyright © 1986 Graziano Gentili and Daniele C. Struppa. 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
Let g,f1,…,fm∈H∞(Δ). We provide conditions on f1,…,fm in order that |g(z)|≤|f1(z)|+…+|fm(z)|, for all z in Δ, imply that g, or g2, belong to the ideal generated by f1,…,fm in H∞.