Volterra type integration operators between weighted Bergman spaces and Hardy 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 \[ J_{g}(f)(z)=\int_{0}^{z}f(λ)g'(λ)dλ\] between weighted Bergman spaces $L_a^p(\omega )$ induced by $\mathcal{D}$ weights and Hardy spaces $H^q$ for $0<p,q<\infty$.