Generalized weighted composition operators from Bloch spaces into Bers-type spaces

Abstract

New criteria for the boundedness and the compactness of the generalized weighted composition operators from Bloch spaces into Bers-type spaces are given in this paper.(

Differences of generalized weighted composition operators from the Bloch space into Bers-type spaces

“…Motivated by these, in this paper, we investigate the boundedness and compactness of the differences of two generalized weighted composition operators from the Bloch space into H ∞ α . The results generalize the corresponding results in [24] on the single generalized weighted composition operator.…”

“…and(19), we obtain|Q k (z)| ≤ C l k B |M u,ϕ (z)|ρ(ϕ(z), ψ(z)) ε.Therefore, from(22),(24) and the discussion of the above cases, we obtain(D n ϕ,u − D n ψ,v )l k H ∞…”

“…In [24], Zhu studied the boundedness and compactness of D n ϕ,u : B → H ∞ α . Motivated by these, in this paper, we investigate the boundedness and compactness of the differences of two generalized weighted composition operators from the Bloch space into H ∞ α .…”

A New Characterization of Generalized Weighted Composition Operators from the Bloch Space into the Zygmund Space

“…Let be a nonnegative integer. The generalized weighted composition operator, denoted by , , is defined as follows (see [4][5][6][7]):…”

Generalized product-type operators from weighted Bergman–Orlicz spaces to Bloch–Orlicz spaces

“…weighted composition operator by Zhu in [65], and studied in [45,55,[61][62][63][65][66][67][68][69]. The product W ϕ,ψ D n can be regarded as a generalization of W ϕ,ψ D. For some other product-type operators, see, for example, [10,[18][19][20][21][34][35][36][37][38]41,42,44,47,[51][52][53]56,57] and the references therein.…”