Growth theorems on classes of normalized locally quasiconformal mappings
Journal Title: Проблемы анализа-Issues of Analysis - Year 2013, Vol 2, Issue 2
Abstract
В классах локально-квазиконформных нормированных автоморфизмов f единичного круга Δ с заданной мажорантой характеристики М. А. Лаврентьева получены асимптотически точные оценки |f(z)|, родственные классическому неравенству А. Мори. The asymptotic sharp growth theorems are proved in the classes of normalized locally quasiconformal automorphisms of the unit disk with the given majorant of the Laurentev's characteristic. The main results are obtained by the means of the methods of extremal lengths, symmetrization and some new method of estimation of distortion of modules of double connected domains under the locally quasiconformal mappings.
Authors and Affiliations
S. U. Graf
Keywords
Related Articles
- EP ID EP234557
- DOI 10.15393/j3.art.2013.2381
- Views 106
- Downloads 0
QUASI-ISOMETRIC MAPPINGS AND THE P-MODULI OF PATH FAMILIES
In this article, we study a connection between quasiisometric mappings of n-dimensional domains and the p-moduli of path families. In particular, we obtain explicit (and sharp) estimates for the distortion of the p-modul...
The Tauberian theorems for the slowly variating with residual functions and their applications
В статье доказываются две тауберовых теоремы для преобразования Лапласа медленно меняющихся с остатком функций и рассматриваются их приложения к суммам значений неотрицательных мультипликативных функций, связанных с проб...
ON THE ALMOST PERIODIC AT INFINITY FUNCTIONS FROM HOMOGENEOUS SPACES
We consider homogeneous spaces of functions defined on the real axis (or semi-axis) with values in a complex Banach space. We study the new class of almost periodic at infinity functions from homogeneous spaces. The main...
GENERIC LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE KAEHLER MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION
Recently, this author studied lightlike hypersurfaces of an indefinite Kaehler manifold endowed with a semi-symmetric non-metric connection in [7]. Further we study this subject. The object of study in this paper is gene...
ON SOME HARMONIC FUNCTIONS RELATED TO HOLOMORPHIC FUNCTIONS WITH A POSITIVE REAL PART
In the paper we examine some holomorphic functions and complex harmonic functions, which satisfy certain conditions of a Mocanu kind. We also consider their relations with appropriate coefficient conditions. The paper is...