Volterra type integration operators between weighted Bergman spaces and Hardy spaces

TL;DR

This paper characterizes when Volterra type integration operators are bounded and compact between weighted Bergman spaces with radial weights satisfying doubling conditions and Hardy spaces, expanding understanding of operator behavior in complex analysis.

Contribution

It provides a complete characterization of boundedness and compactness of Volterra type operators between these specific function spaces under certain weight conditions.

Findings

Characterization of bounded Volterra operators between weighted Bergman and Hardy spaces.

Criteria for compactness of these operators.

Extension of operator theory in weighted analytic function spaces.

Abstract

Let $\mathcal{D}$ be the class of radial weights on the unit disk which satisfy both forward and reverse doubling conditions. Let $g$ be an analytic function on the unit disk $\mathbb{D}$. We characterize bounded and compact Volterra type integration operators \[ J_{g}(f)(z)=\int_{0}^{z}f(\lambda)g'(\lambda)d\lambda \] between weighted Bergman spaces $L_{a}^{p}(\omega )$ induced by $\mathcal{D}$ weights and Hardy spaces $H^{q}$ for $0<p,q<\infty$.