Corrected outer functions

Doubtsov, Evgueni

doi:10.1090/S0002-9939-98-04054-4

Corrected outer functions
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by Evgueni Doubtsov PDF

Proc. Amer. Math. Soc. 126 (1998), 515-522 Request permission

Abstract:

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

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