Aak-theory on Weighted Spaces

A fixed point approach to Nehari’s problem and its applications

We introduce a new approach to Nehari’s problem. This approach is based on some kind of fixed point theorem and allows us to obtain some useful generalizations of Nehari’s and Adamyan – Arov – Krein (AAK) theorems. Among those generalizations: descriptions of Hankel operators in weighted 2 spaces; descriptions of Hankel operators from Dirichlet type spaces to weighted Bergman spaces; commutant ...

A Complete Aak-theorem for Weighted Sequence Spaces

Abstract. We give a full extension of (one version of) the celebrated "AAK-theorem" on Hankel operators, to the case of weighted l-spaces with increasing weights. This theorem was conjectured in [3], and it improves earlier work by S. Treil and A. Volberg, [8]. We also show that the corresponding extension of the classical formulation of the "AAK-theorem" fails, and show that this is a conseque...

Weighted composition operators on weighted Bergman spaces and weighted Bloch spaces

In this paper, we characterize the bonudedness and compactness of weighted composition operators from weighted Bergman spaces to weighted Bloch spaces. Also, we investigate weighted composition operators on weighted Bergman spaces and extend the obtained results in the unit ball of $mathbb{C}^n$.

A special subspace of weighted spaces of holomorphic functions on the upper half plane

In this paper, we intend to define and study concepts of weight and weighted spaces of holomorphic (analytic) functions on the upper half plane. We study two special classes of these spaces of holomorphic functions on the upper half plane. Firstly, we prove these spaces of holomorphic functions on the upper half plane endowed with weighted norm supremum are Banach spaces. Then, we investigate t...

A Note on Weighted Composition Operators on L^p-Spaces