Boundedness and compactness of a new product-type operator from a general space to Bloch-type spaces

Abstract

We characterize the boundedness and compactness of a product-type operator, which, among others, includes all the products of the single composition, multiplication, and differentiation operators, from a general space to Bloch-type spaces. We also give some upper and lower bounds for the norm of the operator. MSC: Primary 47B38; secondary 46E15

Polynomial differentiation composition operators from Besov‐type spaces into Bloch‐type spaces

“…The study of sums of generalized weighted composition operators has been proposed by Stevi ć and Sharma and studied in Stevi ć et al [32,33] and later in Stevi ć et al [34,35]. Specifically, in Stevi ć et al [32][33][34] was studied the operator defined as follows:…”

Generalized Stević-Sharma type operators from derivative Hardy spaces into Zygmund-type spaces

“…), m ∈ N, and investigated its boundedness, essential norm and compactness from Hardy space into the nth weighted-type space, which was introduced by Stević in [25] (see also [26]). In [29], Stević et al introduced the following product-type operator:…”

The Product-Type Operators from Hardy Spaces into n th Weighted-Type Spaces

“…Let m ∈ ℕ 0 , u, v ∈ HðDÞ and φ ∈ SðDÞ be the set of all holomorphic self-map of D. In [6], Stevic′, Sharma and Krishan defined a new product-type operator T m u,v,φ as follows:…”

“…Product-type operators on some spaces of analytic functions on the unit disc have become a subject of increasing interest in the recent years. We refer the reader to [6][7][8][9][10] and the references therein.…”