Abstract
In this current manuscript, some general classes of weighted analytic function spaces in a unit disc are defined and studied. Special functions significant in both analytic T(p,q,m,s;Ψ) norms and analytic Ψ-Bloch norms serve as a framework for introducing new families of analytic classes. An application in operator theory is provided by establishing important properties of the composition-type operator Cϕ such as the boundedness and compactness with the help of the defined new classes.
Highlights
The subjects of complex classes of Banach function spaces and composition operators have gained extremely considerable popularity and high importance during the last few decades
In the last few years, regarding the above-mentioned evolved motivations, some extended complex classes of function spaces associated with certain weights have been introduced and studied actively; see the related references
The main goal of this article is to introduce some new relevant classes of related holomorphic function spaces with the help of some general relevant weights and establish some numerous, potentially useful interesting properties and general formulas
Summary
The subjects of complex classes of Banach function spaces and composition operators have gained extremely considerable popularity and high importance during the last few decades. These important subjects have mainly demonstrated significant applications and interesting, widespread, different fields of mathematical analysis. Some important properties of the composition operator Cφ such as the boundedness and compactness are investigated using the defined general classes in the considered complex disc. For several studies of composition operators on some weighted classes of analytic function spaces, refer to [4,5,6,7,8] and others.
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