TY - JOUR

T1 - Boundary regularity of Nevanlinna domains and univalent functions in model subspaces

AU - Baranov, A.D.

AU - Fedorovskiy, K.Yu.

PY - 2011

Y1 - 2011

N2 - 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 KΘ = H2 ⊖ ΘH2, where Θ 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.

AB - 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 KΘ = H2 ⊖ ΘH2, where Θ 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.

KW - Nevanlinna domain

KW - model subspace KΘ

KW - conformal mapping

KW - inner function

KW - Blaschke product.

U2 - doi:10.1070/SM2011v202n12ABEH004205

DO - doi:10.1070/SM2011v202n12ABEH004205

M3 - статья

VL - 202

SP - 1723

EP - 1741

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 12

ER -