Outer functions in analytic weighted Lipschitz algebras

Details Outer functions in analytic weighted Lipschitz algebras Outer functions in analytic weighted Lipschitz algebras

2010-05-23

arxiv.org/abs/1005.4210v1

Mathematics

Complex Variables

Submitted

Scientific paper

We give a new characterization of outer functions, in analytic weighted
Lipschitz algebras, by their modulus in the boundary. As application, we obtain
a refinement of Shirokov's construction of outer functions vanishing on a given
\omega-Carleson set. We obtain also an extension of
Havin-Shamoyan-Carleson-Jacobs Theorem to an arbitrary modulus of continuity.

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