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Publications (37)
We consider connections between linearly invariant families and Bloch functions defined in the unit disc as well as in a hyperbolic domain. The assumption of uniformly perfectness of a related set is very important.
We consider universal linearly invariant families of mappings defined in the unit ball. We give a connection of such families with Bloch functions, as well as with Bloch mappings.
In this paper, we study the behavior of analytic functions (on the disk) in a Stolz angle. In particular, we prove assertions of the type of the Hardy--Littlewood theorem and obtain estimates for the growth of functions in a Stolz angle.
In this paper we suggest a new definition of the order of a linearly invariant family of locally biholomorphic mappings of the unit ball in . This definition is equivalent to the one given by Pfaltzgraff in [J.A. PfaltzgraffComplex Variables Theory Appl 33 (1997), 239–253.]. It bases on a very simple relationship with the Jacobian of the mappings (...
The paper is concerned with the sharpness of some well-known estimates in universal linear-invariant families
$$\mathcal{U}_\alpha $$
of regular functions. It is shown that the estimate of arg ƒ′(z),z ∈ Δ = {z: z < 1} obtained by Pommerenke in 1964 is sharp; the extremal function is found. A lower estimate for the Schwarzian derivative
in
$$\mathc...
This paper is a continuation of our research [the authors, Proc. 3rd CMFT conference, Nicosia 1997, World Scientific, Ser. Approx. Decompos. 11, 241-257 (1999; Zbl 0943.32003) and Russ. Math. 39, No. 8, 19-30 (1995); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1995, No. 8, 21-33 (1995; Zbl 0855.32001)] concerning the regularity theorems for l...
In this paper we give boundedness criteria for generalized Hankel operators Hf,j and H'f,j
From the text: A computational mistake appeared in the paper. In Theorem 1.2 the conditions for the parameter μ should be written in the following form: ‘μ≠2(1-α) -1 , |μ|≥(α-1) -1 and |μ(α-1)+2|>1’. Moreover, the last sentence in the proof should have the form: ‘By the result of W. C. Royster [Mich. Math. J. 12, 385-387 (1965; Zbl 0193.37301)] we...
We consider the integral means for the class of functions which are meromorphic and univalent in an annulus.
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