Generalized composition operators on Zygmund spaces and Bloch type spaces

Abstract

The boundedness and compactness of the generalized composition operator on Zygmund spaces and Bloch type spaces are investigated in this paper.

Generalized composition operators from area Nevanlinna spaces to Zygmund-type spaces

“…(see for example, [1,2,3]). In [4], the authors defined and studied the generalized composition operator…”

On an integral-type operator from the Bloch space into the QK(p,q) space

“…Let ∈ H(D) and ϕ be an analytic self-map of D. In [6], the author of this paper and Stević defined the generalized composition operator as follows:…”

“…The boundedness and compactness of the generalized composition operator on Zygmund spaces and Bloch spaces were investigated in [6]. Some related results can be found, for example, in [5,7,8,13,16,17,19,30,31].…”

Integral-type operators from a mixed norm space to a bloch-type space on the unit ball

“…Motivated by the fact that composition operators and weighted composition operators naturally come from isometries of some function spaces (see [7]), S. Li and the author introduced the generalized composition operator on H(D) in [8] as follows:…”