## Illinois Journal of Mathematics

### Argument of outer functions on the real line

#### Abstract

A complete description of the modulus of an outer function on the real line is well known. Indeed, this characterization is considered as one of the classical results of the theory of Hardy spaces. However, a satisfactory characterization of the argument of an outer function on the real line is not available yet. In this paper, we define some classes of real functions which can serve as the argument of an outer function. In particular, for any $0 < p \leq \infty$, an increasing bi-Lipschitz function is the argument of an outer function in $H^p(\mathbb{R})$.

#### Article information

Source
Illinois J. Math., Volume 51, Number 2 (2007), 499-511.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138426

Digital Object Identifier
doi:10.1215/ijm/1258138426

Mathematical Reviews number (MathSciNet)
MR2342671

Zentralblatt MATH identifier
1144.42003

Subjects
Primary: 42A50: Conjugate functions, conjugate series, singular integrals
Secondary: 30D55

#### Citation

Mashreghi, Javad; Pouryayevali, Mohamad Reza. Argument of outer functions on the real line. Illinois J. Math. 51 (2007), no. 2, 499--511. doi:10.1215/ijm/1258138426. https://projecteuclid.org/euclid.ijm/1258138426