Essential Norms and Schatten(-Herz) Classes of Integration Operators from Bergman Spaces to Hardy Spaces

Abstract

In this paper, we completely characterize the compactness of the Volterra type integration operators $J_b$ acting from weighted Bergman spaces $A_\alpha^p$ to Hardy spaces $H^q$ for all $0<p, q<\infty$. Furthermore, we give some estimates for the essential norms of $J_b: A_\alpha^p \rightarrow H^q$ in the case $0<p \leq q<\infty$. We finally describe the membership in the Schatten(-Herz) class of the Volterra type integration operators.