Authors: | Stević, Stevo | Title: | Weighted integrals of holomorphic functions on the polydisc | Journal: | Zeitschrift fur Analysis und ihre Anwendung | Volume: | 23 | Issue: | 3 | First page: | 577 | Last page: | 587 | Issue Date: | 1-Jan-2004 | Rank: | M23 | ISSN: | 0232-2064 | DOI: | 10.4171/ZAA/1211 | Abstract: | We show that a holomorphic function on the unit polydisc Un in Cn belongs to the weighted Bergman space Aαp(Un), when p ∈ (0, 1], if and only if all weighted derivations of order |k| (with positive orders of derivations) belong to the related weighted Lebesgue space Lαp(Un). This result extends Theorem 1.8 by Benke and Chang in [Nagoya Math. J. 159 (2000), 25-43]. |
Keywords: | Holomorphic function | Polydisc | Weighted Bergman space | Publisher: | European Mathematical Society |
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