Products of differentiation, composition and multiplication from Bergman type spaces to Bers type spaces

Products of differentiation and composition operators on the Bloch space

“…The boundedness and compactness of the operators DC φ and C φ D on Hardy and Bergman spaces were investigated in [2] and [7]. Recently, several authors have studied these operators, one can refer to [3][4][5][6][7][8] and [10].…”

Weighted differentiation composition operators from weighted bergman space to n th weighted space on the unit disk

“…From those studies, they gave some sufficient and necessary conditions for these operators to be bounded and compact. Concerning these results, we also recommend the interested readers to ( [3][4][5][6][7][8][9] …”

Composition Followed by Differentiation Between H ∞ and Zygmund Spaces

“…Motivated by paper [20], Stević in [30] calculated Hilbert-Schmidt norms of products of composition and differentiation operators on the Bergman space A 2 α (α > −1) and the Hardy space H 2 on the unit disk, studied when the convergence of sequences (ϕ n ) of symbols to a given symbol ϕ implies the convergence of product operators C ϕ n D k , and characterized the boundedness and compactness of the operator C ϕ D k : A 2 α → A 2 α in terms of the generalized Nevanlinna counting function. Zhu in [39] completely characterized boundedness and compactness for linear operators which were obtained by taking products of differentiation, composition and multiplication operators and which act from Bergman type spaces to Bers spaces. Kumar and Singh investigated the same problem for operators DC ϕ M ψ acting on A p α and used the Carleson-type conditions.…”