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 Open image in new window with p, q ∈ [1,∞) and α = (α1, ..., αn) such that αj > −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 ∈ Open image in new window , where \( \vec q \) = (q, ..., q).