Boundedness and compactness of an integral operator between H ^∞ and a mixed norm space on the polydisk

Abstract

This addendum to [1] completely characterizes the boundedness and compactness of a recently introduced integral type operator from the space of bounded holomorphic functions H ^∞($\mathbb{D}^n$) on the unit polydisk $\mathbb{D}^n$ to the mixed norm space

with p, q ∈ [1,∞) and α = (α₁, ..., α _n ) such that α _j > −1 for every j = 1, ..., n. We show that the operator is bounded if and only if it is compact and if and only if g ∈

, where $\vec q$ = (q, ..., q).