On a generalization of the corona problem

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∞.