Stevic-Sharma operators from area Nevanlinna spaces to Bloch-Orlicz type spaces

Abstract

Let D be the open unit disk in the complex plane C, H(D) the class of all analytic functions on D and ϕ an analytic self-map of D. In order to unify the products of composition, multiplication, and differentiation operators, Stević and Sharma introduced the following so-called Stević-Sharma operator on H(D):where ψ 1 , ψ 2 ∈ H(D). By constructing some more suitable test functions in the area Nevanlinna space, the boundedness and compactness of the Stević-Sharma operator from the area Nevanlinna space to the Bloch-orlicz space and the little Bloch-orlicz space are characterized.

On Stević-Sharma Operators from General Class of Analytic Function Spaces into Zygmund-Type Spaces

“…Over the past 10 years, the boundedness and compactness of this operator have been studied extensively in the most well-known spaces of analytic functions; for example, see [5,9]. This paper proceeds as follows.…”

Product Type Operators Involving Radial Derivative Operator Acting between Some Analytic Function Spaces

“…The product-type operators W φ,ξ D and DW φ,ξ were respectively, considered in [2] and [3]. To characterize the product-type operators in a unified way, new product-type operator T φ 1 ,φ 2 ,ξ was introduced which can be found in [9,10] and the references therein.…”