Volterra-Composition Operators Acting on $S^{p}$ Spaces and Weighted Zygmund Spaces (European Journal of Pure and Applied Mathematics, 2024)
Let $φ$ be an analytic selfmap of the open unit disk $\mathbb{D}$ and $g$ be an analytic function on $\mathbb{D}$. The Volterra-type composition operators induced by the maps $g$ and $φ$ are defined as $$\left(I_{g}^{φ}f\right)(z)= \int_{0}^{z} f^{′}(φ(ζ)) g(ζ) dζ \hspace{0.07in} \text{and} \hspace{0.07in} \left(T_{g}^{φ}f\right)(z)= \int_{0}^{z} f(φ(ζ)) g^{′}(ζ) dζ .$$For $1≤ p
Keywords: Weighted Zygmund Spaces; $S^p$ spaces; Volterra operators; composition operators; bounded operators; compact operators