Generalized Weighted Composition Operators From Area Nevanlinna Spaces to Weighted-Type Spaces

Abstract

Let H(D) denote the class of all analytic functions on the open unit disk D of the complex plane C. Let n be a nonnegative integer, φ be an analytic self-map of D and u ∈ H(D). The generalized weighted composition operator is defined by D n φ,u f = uf (n) • φ, f ∈ H(D). The boundedness and compactness of the generalized weighted composition operator from area Nevanlinna spaces to weighted-type spaces and little weighted-type spaces are characterized in this paper.

Stevic-Sharma operators from area Nevanlinna spaces to Bloch-Orlicz type spaces

“…We can prove (24) similarly to (22), hence we omit. Next we prove (25). Take h 2 (z) = z 2 ∈ N p α .…”

“…If p = 1, it becomes the weighted Bergman-Nevanlinna space. For some results on these spaces and some concrete operators on them can be found, for example, in [20,25,26] and the references therein.…”

“…The generalized weighted composition operators D n ϕ,ψ f = ψf (n) • ϕ from area Nevanlinna spaces to weighted-type spaces and Bloch-type spaces were studied in [25] and [26], respectively. By constructing some more suitable test functions in the area Nevanlinna space, in this paper we characterize the boundedness and compactness of the Stević-Sharma operator from the area Nevanlinna space to the Bloch-orlicz space and the little Bloch-Orlicz space.…”