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

Abstract

Abstract. In this paper, we characterize the boundedness, compactness and essential norm of products of differentiation and composition operators from the Bloch space and weighted Dirichlet spaces to analytic Morrey type spaces.

On a linear operator between weighted‐type spaces of analytic functions

“…Product‐type operators containing these, and some other linear operators, have been investigated a lot. Besides weighted composition operators, the products $$$ D{C}_{\varphi } $$$ and $$$ {C}_{\varphi }D $$$ have attracted some attention (see, e.g., earlier studies [3–7] and the related references therein). The following product‐type operator $$$ {D}_{\varphi, u}^m:= {M}_u{C}_{\varphi }{D}^m $$$ has been investigated in previous research [8–16].…”

“…For some recent investigations of the boundedness and compactness of various concrete linear operators on spaces of holomorphic functions on domains in $$$ \mathrm{\mathbb{C}} $$$ or $$$ {\mathrm{\mathbb{C}}}^n $$$, see, for instance, earlier studies [3–34, 41–43, 47–50], as well as many related references quoted therein.…”

Metrical Boundedness and Compactness of a New Operator between Some Spaces of Analytic Functions

“…Let us briefly mention a part of the investigations preceding the one in the paper. Of the product-type operators containing the differential one, first were studied the operators DC ϕ and C ϕ D (see, e.g., [6][7][8][9][10][11] and the related references therein). In [12] was studied the product of the multiplication operator followed by the differentiation one on the Bloch-type spaces.…”

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

“…After the publication of [7], some experts started studying product-type operators involving the differentiation operator (see, e.g., [14-16, 18, 44]). Some of these papers study the operators from or to Bloch-type and/or Zygmund-type spaces ( [2,4,6,8,9,17,20,29,50]).…”