On generators in ideals of entire functions of finite order and type on the plane.
On harmonic conjugates with exponential mean growth
On linear functionals in Hardy-Orlicz spaces, I
On linear functionals in Hardy-Orlicz spaces, II
On linear functionals in Hardy-Orlicz spaces. III
On maximal and complete regions
On products of some Toeplitz operators on polyanalytic Fock spaces
The purpose of this paper is to study the Sarason’s problem on Fock spaces of polyanalytic functions. Namely, given two polyanalytic symbols and , we establish a necessary and sufficient condition for the boundedness of some Toeplitz products subjected to certain restriction on and . We also characterize this property in terms of the Berezin transform.
On some classes of holomorphic vector functions
On some new sharp embedding theorems in minimal and pseudoconvex domains
We present new sharp embedding theorems for mixed-norm analytic spaces in pseudoconvex domains with smooth boundary. New related sharp results in minimal bounded homogeneous domains in higher dimension are also provided. Last domains we consider are domains which are direct generalizations of the well-studied so-called bounded symmetric domains in Our results were known before only in the very particular case of domains of such type in the unit ball. As in the unit ball case, all our proofs are...
On some new theorems on certain analytic and meromorphic classes of Nevanlinna type on the complex plane
On some problems connected with diagonal map in some spaces of analytic functions
For any holomorphic function on the unit polydisk we consider its restriction to the diagonal, i.e., the function in the unit disc defined by , and prove that the diagonal map maps the space of the polydisk onto the space of the unit disk.
On some spaces of holomorphic functions of exponential growth on a half-plane
In this paper we study spaces of holomorphic functions on the right half-plane R, that we denote by Mpω, whose growth conditions are given in terms of a translation invariant measure ω on the closed half-plane R. Such a measure has the form ω = ν ⊗ m, where m is the Lebesgue measure on R and ν is a regular Borel measure on [0, +∞). We call these spaces generalized Hardy–Bergman spaces on the half-plane R. We study in particular the case of ν purely atomic, with point masses on an arithmetic progression...
On the Analogue of Koebe's Theorem for Functions with Values in a Clifford Algebra.
On the characteristic properties of certain optimization problems in complex analysis
We shall be concerned in this paper with an optimization problem of the form: J(f) → min(max) subject to f ∈ 𝓕 where 𝓕 is some family of complex functions that are analytic in the unit disc. For this problem, the question about its characteristic properties is considered. The possibilities of applications of the results of general optimization theory to such a problem are also examined.
On the convolution of analytic functions.
On the diametral dimension of weighted spaces of analytic germs
We prove precise estimates for the diametral dimension of certain weighted spaces of germs of holomorphic functions defined on strips near ℝ. This implies a full isomorphic classification for these spaces including the Gelfand-Shilov spaces and for α > 0. Moreover we show that the classical spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions are not isomorphic.
On the generalized Hardy spaces.
On the isomorphic classification of weighted spaces of holomorphic functions
On the norm of certain weighted composition operators on the Hardy space.
On the powers of quasihomogeneous Toeplitz operators
We present sufficient conditions for the existence of th powers of a quasihomogeneous Toeplitz operator , where is a radial polynomial function and , are natural numbers. A large class of examples is provided to illustrate our results. To our best knowledge those examples are not covered by the current literature. The main tools in the proof of our results are the Mellin transform and some classical theorems of complex analysis.