Open AccessWeighted Integrals of Holomorphic Functions on the Polydisc II
Author(s) -
Stevo Stević
Publication year - 2004
Publication title -
zeitschrift für analysis und ihre anwendungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.567
H-Index - 35
eISSN - 1661-4534
pISSN - 0232-2064
DOI - 10.4171/zaa/1222
Subject(s) - polydisc , holomorphic function , mathematics , pure mathematics , mathematical analysis
We show that a holomorphic function on the unit polydisc Un in C belongs to the weighted Bergman space Aα(U), 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 Lα(U). This result extends Theorem 1.8 by Benke and Chang in [Nagoya Math. J. 159 (2000), 25 – 43].
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