Abstract This paper characterises the boundedness and compactness of Agler–McCarthy monomial operators by reducing them to weighted composition deriving explicit Carleson measure criteria on half-plane. The results are illustrated examples.

Let V be an arbitrary system of weights on an open connected subset G of CN (N ≥ 1) and let B (E) be the Banach algebra of all bounded linear operators on a Banach space E. Let HVb (G, E) and HV0 (G, E) be the weighted locally convex spaces of vector-valued analytic functions. In this paper, we characterize self-analytic mappings φ : G → G and operator-valued analytic mappings Ψ : G → B (E) whi...

We determine the spectra of weighted composition operators acting on the weighted Banach spaces of analytic functions H∞ vp when the symbol φ has a fixed point in the open unit disk. Further, we apply this result to give the spectra of composition operators on Bloch type spaces. In particular, we answer in the affirmative a conjecture by MacCluer and Saxe.

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.