Corrected outer functions

Abstract

Given 0 > p > 2 0>p>2 and a strictly positive continuous function φ \varphi on the unit circle, we construct a bounded analytic function g g such that | g ∗ | = φ |g^{*}|=\varphi a.e., and g g is in the Besov space A p 1 A_{p}^{1} on the unit disc.