Boundary regularity of Nevanlinna domains and univalent functions in model subspaces

A. D. Baranov   ; K. Yu. Fedorovskiy

Sbornik. Mathematics, Tome 202 (2011) no. 12, pp. 1723-1740

Résumé

In the paper we study boundary regularity of Nevanlinna domains, which have appeared in problems of uniform approximation by polyanalytic polynomials. A new method for constructing Nevanlinna domains with essentially irregular nonanalytic boundaries is suggested; this method is based on finding appropriate univalent functions in model subspaces, that is, in subspaces of the form $K_\varTheta=H^2\ominus\varTheta H^2$, where $\varTheta$ is an inner function. To describe the irregularity of the boundaries of the domains obtained, recent results by Dolzhenko about boundary regularity of conformal mappings are used. Bibliography: 18 titles.

Détail

Keywords: model subspace $K_\varTheta$, conformal mapping, inner function, Blaschke product.
Mots-clés : Nevanlinna domain

Bibliographie

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