Authors: | Stević, Stevo | Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | Boundedness and compactness of an integral operator between H ∞ and a mixed norm space on the polydisk | Journal: | Siberian Mathematical Journal | Volume: | 50 | Issue: | 3 | First page: | 495 | Last page: | 497 | Issue Date: | 1-Jun-2009 | Rank: | M23 | ISSN: | 0037-4466 | DOI: | 10.1007/s11202-009-0055-y | 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). |
Keywords: | Bounded analytic function | Boundedness | Compactness | Integral operator | Mixed norm space | Polydisk | Publisher: | Springer Link |
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