Asymmetric Truncated Hankel Operators: Rank One, Matrix Representation

Asymmetric truncated Hankel operators are the natural generalization of truncated Hankel operators. In this paper, we determine all rank one operators of this class. We explore these operators on finite-dimensional model spaces, in particular, their matrix representation. We also give their matrix representation and the one for asymmetric truncated Toeplitz operators in the case of model spaces associated to interpolating Blaschke products.

Multipliers and closures of Besov-type spaces in the Bloch space

Let p > 1 and let ? be a non-negative function defined in R+. A function f ? H(D) belongs to the space Bp(?) (see [4]) if ||f||p Bp(?) = |f(0)jp + ?D |(1-|z|2) f?(z)|p ?(1-|z|2)/(1-|z|2)2 dA(z) < ?. In this paper, motivated by the works of B?koll? and Bao and G???s, under some conditions on the weight function ?, we investigate the closures CB(B ? Bp(?)) of the spaces B ? Bp(?) in the Bloch space. Moreover we prove that interpolating Blaschke products in CB(B ? Bp(?)) are multipliers of Bp(?) ? BMOA.

Boundary interpolation and approximation by infinite Blaschke products

This paper considers the problem of boundary interpolation (in the sense of non-tangential limits) by Blaschke products and interpolating Blaschke products. Simple and constructive proofs, which also work in the more general situation of $H^\infty(\Omega)$ where $\Omega$ is a more general domain, are given of a number of results showing the existence of Blaschke products solving certain interpolation problems at a countable set of points on the circle. A variant of Frostman's theorem is also presented.

Blaschke products in Lipschitz spaces

We study the membership of Blaschke products in Lipschitz spaces, especially for interpolating Blaschke products and for those whose zeros lie in a Stolz angle. We prove several theorems that complement or extend the earlier works of Ahern and the author.

INTEGRABILITY OF THE DERIVATIVE OF A BLASCHKE PRODUCT

We study the membership of derivatives of Blaschke products in Hardy and Bergman spaces, especially for the the interpolating Blaschke products and for those whose zeros lie in a Stolz domain. We obtain new and very simple proofs of some known results and prove new theorems that complement or extend the earlier works of Ahern, Clark, Cohn, Kim, Newman, Protas, Rudin, Vinogradov and others.