Illinois Journal of Mathematics

Univalent functions, Hardy spaces and spaces of Dirichlet type

Albert Baernstein, Daniel Girela, and José Ángel Peláez

Full-text: Open access

Abstract

We prove that for $p\in (0,\infty)$ an analytic univalent function in the unit disk belongs to the Hardy space $H^p$ if and only if it belongs to the Dirichlet type space $\mathcal {D}_{p-1}^p$.

Article information

Source
Illinois J. Math., Volume 48, Number 3 (2004), 837-859.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258131055

Mathematical Reviews number (MathSciNet)
MR2114254

Zentralblatt MATH identifier
1063.30014

Subjects
Primary: 30H05: Bounded analytic functions
Secondary: 30C35: General theory of conformal mappings 30D55 31C25: Dirichlet spaces 46E15: Banach spaces of continuous, differentiable or analytic functions

Citation

Baernstein, Albert; Girela, Daniel; Peláez, José Ángel. Univalent functions, Hardy spaces and spaces of Dirichlet type. Illinois J. Math. 48 (2004), no. 3, 837--859. https://projecteuclid.org/euclid.ijm/1258131055


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