On the range of analytic functions related to Caratheodory class
Optimal Sampling of Holomorphic Fuctions. II.
Orthogonal polynomials and middle Hankel operators on Bergman spaces
We introduce a sequence of Hankel style operators , k = 1,2,3,..., which act on the Bergman space of the unit disk. These operators are intermediate between the classical big and small Hankel operators. We study the boundedness and Schatten-von Neumann properties of the and show, among other things, that are cut-off at 1/k. Recall that the big Hankel operator is cut-off at 1 and the small Hankel operator at 0.
Pointwise inequalities of logarithmic type in Hardy-Hölder spaces
We prove some optimal logarithmic estimates in the Hardy space with Hölder regularity, where is the open unit disk or an annular domain of . These estimates extend the results established by S. Chaabane and I. Feki in the Hardy-Sobolev space of the unit disk and those of I. Feki in the case of an annular domain. The proofs are based on a variant of Hardy-Landau-Littlewood inequality for Hölder functions. As an application of these estimates, we study the stability of both the Cauchy problem...
Regularization of one class of difference equations.
Representations of Inverse Functions by the Integral Transform with the Sign Kernel
Mathematics Subject Classification: Primary 30C40In this paper we give practical and numerical representations of inverse functions by using the integral transform with the sign kernel, and show corresponding numerical experiments by using computers. We derive a very simple formula from a general idea for the representation of the inverse functions, based on the theory of reproducing kernels.
Reproducing kernels and multiple interpolation by holomorphic functions
Schwarzian derivatives, the Poincaré metric and the kernel function.
Some applications of the theorem on rational approximation in the mean
Some Hölder-logarithmic estimates on Hardy-Sobolev spaces
We prove some optimal estimates of Hölder-logarithmic type in the Hardy-Sobolev spaces , where , and is either the open unit disk or the annular domain , of the complex space . More precisely, we study the behavior on the interior of of any function belonging to the unit ball of the Hardy-Sobolev spaces from its behavior on any open connected subset of the boundary of with respect to the -norm. Our results can be viewed as an improvement and generalization of those established...
Some Inequalities for Analytic Functions with a Finite Dirichlet Integral on the Unit Disc.
Some isometrical identities in the wave equation.
Szegő projections for Hardy spaces of monogenic functions and applications.
The Berezin transform and operators on spaces of analytic functions
In this article we will illustrate how the Berezin transform (or symbol) can be used to study classes of operators on certain spaces of analytic functions, such as the Hardy space, the Bergman space and the Fock space. The article is organized according to the following outline. 1. Spaces of analytic functions 2. Definition and properties Berezin transform 3. Berezin transform and non-compact operators 4. Commutativity of Toeplitz operators 5. Berezin transform and Hankel or Toeplitz operators 6....
The Bergman and Schiffer transforms on weighted norm spaces
The Cauchy Kernel, the Szegö Kernel, and the Riemann Mapping Function.
The Poisson extension of K -quasihomography on the unit circle
In this paper some estimates for the Poisson extension of a K-quasihomography on the unit circle are given.
Uniqueness theorems for almost analytic functions and their use in approximation theory and in the theory of Toeplitz operators
Граничные свойства аналитических функций, представимых интегралами типа Коши
К теории квазиконформных отображений