Let $$\mu _\alpha$$ be the Lebesgue plane measure on unit disk with radial weight $$\frac{\alpha +1}{\pi }(1-|z|^2)^\alpha$$ . Denote by $${\mathcal {A}}^{2}_{n}$$ space of n-analytic functions $${\mathbb {D}}$$ , square-integrable respect to Extending results Ramazanov (1999, 2002), we explain that polynomials (studied Koornwinder in 1975 and Wünsche 2005) form an orthonormal basis Using this ...

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 ...

In this paper, we study the weighted composition operators Wφ,ψ :f → ψ(f ◦ φ) between weighted Bergman spaces and Hardy spaces on the unit ball of Cn. We characterize the boundedness and the compactness of the weighted composition operators Wφ,ψ :Ap(να)→Aq(νβ) (0 < q < p <∞, −1 < α,β <∞) and Wφ,ψ :Hp(B)→Hq(B) (0 < q < p <∞). © 2006 Elsevier Inc. All rights reserved.

We study the backward shift operator on Hilbert spaces Hα (for α ≥ 0) which are norm equivalent to the Dirichlet-type spaces Dα. Although these operators are unitarily equivalent to the adjoints of the forward shift operator on certain weighted Bergman spaces, our approach is direct and completely independent of the standard Cauchy duality. We employ only the classical Hardy space theory and an...

In this paper, we estimate essential norms of weighted composition operators and differences two on the Bergman spaces in unit ball.