Anton Baranov

Embeddings of model subspaces of the Hardy space: compactness and Schatten-von Neumann ideals

We study embeddings of model (star-invariant) subspaces K Θ of the Hardy space Hp, associated with an inner function Θ. We obtain a criterion for the compactness of the embedding of K Θ into L p(μ) analogous to the Volberg–Treil theorem on bounded embeddings and answer a question posed by Cima and Matheson. The proof is based on Bernstein inequalities for functions in K Θ. Also we study measures μ such that the embedding operator belongs to a Schatten–von Neumann ideal.

Linear and Complex Analysis: Dedicated to V. P. Havin on the Occasion of His 75th Birthday

Includes articles by friends and collaborators of a renowned Russian mathematician V P Havin, prepared on the occasion of Havins 75th birthday. This book presents articles devoted to areas of analysis where Havin himself worked successfully for many years.

Boundary properties of Green functions in the plane

We study the boundary properties of the Green function of bounded simply connected domains in the plane. Essentially, this amounts to studying the conformal mapping taking the unit disk onto the domain in question. Our technique is inspired by a 1995 article of Jones and Makarov [11]. The main tools are an integral identity as well as a uniform Sobolev embedding theorem. The latter is in a sense dual to the exponential integrability of Marcinkiewicz-Zygmund integrals. We also develop a Grunsky identity, which contains the information of the classical Grunsky inequality. This Grunsky identity is the case where p = 2 of a more general Grunsky identily for L-p-spaces.

Completeness and Riesz bases of reproducing kernels in model subspaces

We use the recent approach of N. Makarov and A. Poltoratski to give a criterion of completeness of systems of reproducing kernels in the model subspaces KΘ = H 2aΘH2 of the Hardy class H. As an application we prove new results on stability of completeness with respect to small perturbations and obtain criteria of completeness in terms of certain densities. We also obtain a description of systems of reproducing kernels corresponding to real points which form a Riesz basis in a given model subspace. 2000 MSC. Primary: 30H05, 46E22; secondary: 30D50, 30D55, 47A15.

Weighted norm inequalities for de Branges-Rovnyak spaces and their applications

Let

Subspaces of de Branges spaces with prescribed growth

{\cal H}(b)

Localization of Zeros for Cauchy Transforms

denote the de Branges--Rovnyak space associated with a function

Weighted Bernstein-type inequalities, and embedding theorems for the model subspaces

b

On perturbations of the group of shifts on the line by unitary cocycles

in the unit ball of

Summability properties of Gabor expansions

H^\infty({\Bbb C}_+)