1. Volterra-Composition Operators Acting on Sp Spaces and Weighted Zygmund Spaces.
- Author
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Al-Rawashdeh, Waleed
- Subjects
- *
COMPOSITION operators , *ANALYTIC functions , *HARDY spaces , *ANALYTIC spaces , *VOLTERRA operators , *CONTINUOUS functions - Abstract
Let φ be an analytic selfmap of the open unit disk D and g be an analytic function on D. The Volterra-type composition operators induced by the maps g and φ are defined as (Ig φ f) (z) = ∫0 z f' (φ(ζ))g(ζ)dζ and (Tg φf) (z) = ∫0 z f(φ(ζ))g′ (ζ)dζ. For 1 ≤ p < ∞, S p (D) is the space of all analytic functions on D whose first derivative f ′ lies in the Hardy space Hp (D), endowed with the norm ∥f∥Sp = |f(0)| + ∥f′ ∥Hp . Let µ : (0, 1] → (0, ∞) be a positive continuous function on D such that for z ∈ D we define µ(z) = µ(|z|). The weighted Zygmund space Zµ(D) is the space of all analytic functions f on D such that supz∈D µ(z)|f ′′(z)| is finite. In this paper, we characterize the boundedness and compactness of the Volterra-type composition operators that act between S p spaces and weighted Zygmund space [ABSTRACT FROM AUTHOR]
- Published
- 2024
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