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

Abstract

A new criterion for the boundedness and the compactness of the generalized weighted composition operators from the Bloch space into the Zygmund space is given in this paper.

Generalized weighted composition operators from the Bloch-type spaces to theweighted Zygmund spaces

“…The equivalence of conditions (a), (b) and (d) of corollaries 3.3 and 3.4 was proved in [4]. Also Stević in [10] proved that the conditions (a), (b) and (e) of above two corollaries are equivalent.…”

Products of Differentiation and Composition Operators From the Bloch Space and Weighted Dirichlet Spaces to Morrey Type Spaces

“…If n = 1, we get the operator C ϕ D, which was studied in [4,5,6,7,8,14,15,17,24,25]. In [13], Smith and Zhao characterized the boundedness and compactness of C ϕ : B → Q p .…”

The product-type operators from logarithmic Bloch spaces to Zygmund-type spaces

“…Note that, for ψ 2 ≡ 0, we obtain the weighted differentiation composition operator. For some later results on the weighted differentiation composition operator on various spaces of analytic functions see, e.g., [11,23,31,51,[58][59][60].…”