Boundary regularity of Nevanlinna domains and univalent functions in model subspaces

Abstract

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 , where 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.