Products of differentiation and composition operators on the Bloch space

Abstract

We consider linear product operators DC φ and C φ D m acting on the Bloch space, where C φ is the composition operator and D m is the differentiation operator. The compactness criteria of the operators DC φ and C φ D m on the Bloch space are established in terms of the norms of φ n in the Bloch space.

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 .…”

Weighted differentiation composition operator from logarithmic Bloch spaces to Bloch‐type spaces

“…Concerning the composition operator from log‐Bloch space to μ‐Bloch space, we refer the readers into the papers , . Moreover, the papers , , , , are also about the new subject, which are helpful for our study. Based on the above foundations, the goal of this paper is to give a new characterization for the weighted differentiation operator on the unit disk.…”

New Characterizations of Composition Operators Between Bloch Type Spaces in the Unit Ball

“…In [18], Wulan, Zheng and Zhu obtained a new result about the compactness of the composition operator on the Bloch space in the unit disk. Recently, interest has arisen to characterize the boundedness and compactness of (weighted) composition operators (u)C ϕ on Bloch type spaces in terms of the n-th power of the analytic self-map ϕ on the unit disc D, such as [4,7,8,9,10,12,17,19].…”