The s- Generalized Composition Operators from B(m,n) → Q Spaces gP

Let φ and ψ be analytic self-maps of the open unit disk D . Using pseudo-hyperbolic distance ρ(φ ,ψ) , we characterize the boundedness and compactness of the differences of generalized composition operators (C φ −Ch ψ ) f (z) = ∫ z 0 [ f ′(φ(ξ ))g(ξ )− f ′(ψ(ξ ))h(ξ )]dξ , z ∈ D between two Bloch-type spaces on D . The results generalize the corresponding results on the single generalized composition operator and on the differences of generalized composition operators on the Bloch space. Mathematics subject classification (2010): Primary 47B38; secondary 30H30.

We calculate the essential norm of some extensions of the generalized composition operators between kth weighted-type spaces on the unit disk in the complex plane, considerably extending some results in the literature.

Let0<p<∞, let-2<q<∞, and letφbe an analytic self-map of𝔻andg∈H(𝔻). The boundedness and compactness of generalized composition operators(Cφgf)(z)=∫0z‍f'(φ(ξ))g(ξ)dξ, z∈𝔻, f∈H(𝔻), fromℬμ(ℬμ,0) spaces toQK,ω(p,q)spaces are investigated.

The present paper introduces the class of weighted generalized composition operators of higher order defined on the weighted Hardy spaces. The study of bounded operators belonging to this class is undertaken and an attempt is made to describe their structural and spectral properties.