Domination on sets and in \(H^p\) (Q1266936)

The authors have characterized the subset \(E\) of the unit dik with the following property: if \(f\) is a function of the Hardy space \(H^p\), \(0<p\leq\infty\), and \(0<\| f\|_p< c<\infty\) then there exists the function \(g\in H^p\) such that \(| g(z)|\leq| f(z)|\) on \(E\) and \(\| g\|_p= c\).