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 ∞( Dn ) on the unit polydisk Dn to the mixed norm space Aαp,q Dn 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 Aα+qp,q Dn, where q = (q, ..., q).