Interpolation between Hardy spaces on circular domains with applications to approximation (Q1599479)

The authors give interpolation between Hardy spaces \(H^2\) and \(H^\infty\) on circular domains. As the first application, they show a very explicit version of the Nehari approximation theorem in order to obtain an analytic approximation to a given function which is to be nearly optimal in both \(L^\infty\) and \(L^2\) norms. As the second application, they give somewhat sharper forms of so-called ``correction'' theorems, whereby an \(H^p\) function for \(1<p< \infty\) is approximated by an \(H^\infty\) function with small \(H^2\) error.