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

Abstract

A Stevi c ′ -Sharma operator denoted by T ψ 1 , ψ 2 , φ is a generalization product of multiplication, differentiation, and composition operators. In this paper, we characterize the bounded and compact Stevi c ′ -Sharma operator T ψ 1 , ψ 2 , φ from a general class X of Banach function spaces into Zygmund-type spaces with some of the most convenient test functions on the open unit disk. Using several restrictive terms, we show that all bounded operators T ψ 1 , ψ 2 , φ from X into the little Zygmund-type spaces are compact. As an application, we show that our results hold up for some other domain spaces of T ψ 1 , ψ 2 , φ , such as the Hardy space and the weighted Bergman space.

Norms of Composition Operators from Weighted Harmonic Bloch Spaces into Weighted Harmonic Zygmund Spaces

“…In [1], the second author discusses the essential norms of Stević-Sharma operators from general Banach spaces into Zygmund-type spaces, and in [2], the authors characterize the bounded and compact Stević-Sharma operator from a general class X of Banach function spaces into Zygmundtype space. In [3], the authors show a new essential norm estimate of composition operators from weighted Bloch space into μ-Bloch spaces.…”

Composition Operators From Harmonic Lipschitz Space Into Weighted Harmonic Zygmund Space

“…The operator theory has been characterized for spaces of analytic functions with different settings, and a significant number of related papers have appeared in the literature (see, for example, [7], [8], [10], [13], [17], and [22]). However, a similar investigation of the harmonic setting remains limited, see [2] and [14].…”