ON SOME CLASSES OF HARMONIC FUNCTIONS WITH CONDITIONS IMPOSED ON COEFFICIENTS AND THEIR ARGUMENTS
Journal Title: Проблемы анализа-Issues of Analysis - Year 2006, Vol 13, Issue
Abstract
In this paper we consider a few classes of functions f harmonic in the unit disc ∆ of the form f = h+ \overline{g}, where h, g are suitably normalized functions holomorphic in ∆. Our special attention is drawn to some classes generated by respective coefficient conditions and to classes of functions with conditions imposed on coefficient arguments. We examine relationships between these conditions and some analytic conditions of stalikeness or convexity of considered functions.
Authors and Affiliations
Z. J. JAKUBOWSKI, A. LAZINSKA
Keywords
Related Articles
- EP ID EP243951
- DOI -
- Views 92
- Downloads 0
KOEBE DOMAINS FOR THE CLASS OF TYPICALLY REAL ODD FUNCTIONS
In this paper we discuss the generalized Koebe domains for the class T^(2) and the set D ⊂ Δ = {z in C : |z| < 1}, i.e. the sets of the form T f in TM f(D). The main idea we work with is the method of the envelope. We de...
ON DECRIPTIONS OF CLOSED IDEALS OF ANALYTIC AREA NEVANLINNA TYPE CLASSES IN A CIRCULAR RING ON A COMPLEX PLANE C
We define certain new large area Nevanlinna type spaces in circular ring K on a complex plane and provide complete decriptions of ideals of these new scales of spaces. Our results extend some previously known assertions.
ОБ ОБЛАСТЯХ, КОНФОРМНО ИЗОМОРФНЫХ ПЛОСКОСТИ С РАЗРЕЗАМИ ВДОЛЬ ПРЯМОЙ
It is proved that extended complex plane with n slits on the real axis is conformally isomorphed to a circular domain, symmetric with respect to this axis.
Sobolev-Orthonormal System of Functions Generated by the System of Laguerre Functions
We consider the system of functions λ α r,n (x) (r ∈ N, n = 0, 1, 2, . . .), orthonormal respect to the Sobolev-type inner product f, g = Σ r-1 ν=0 f (υ) (0) g (υ) (0)+ I ∞ 0 f (r) (x) g (r) (x) dx and generated by the o...
Multivariate Iyengar type inequalities for radial functions
Here we present a variety of multivariate Iyengar type inequalities for radial functions defined on the shell and ball. Our approach is based on the polar coordinates in R^N, N>=2, and the related multivariate polar inte...