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Zeitschrift für Analysis und ihre Anwendungen

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Volume 23, Issue 3, 2004, pp. 577–587
DOI: 10.4171/ZAA/1211

Published online: 2004-09-30

Weighted Integrals of Holomorphic Functions on the Polydisc

Stevo Stevic[1]

(1) Serbian Academy of Science, Beograd, Serbia

We show that a holomorphic function on the unit polydisc $U^n$ in ${\bf C}^n$ belongs to the weighted Bergman space ${\cal A}^p_{\alpha}(U^n)$, when $p\in (0,1],$ if and only if all weighted derivations of order $|k|$ (with positive orders of derivations) belong to the related weighted Lebesgue space ${\cal L}^p_{\alpha}(U^n).$ This result extends Theorem 1.8 by Benke and Chang in their recent paper which appeared in Nagoya Math. J. 159 (2000), 25--43.

Keywords: Holomorphic function, weighted Bergman space, polydisc

Stevic Stevo: Weighted Integrals of Holomorphic Functions on the Polydisc. Z. Anal. Anwend. 23 (2004), 577-587. doi: 10.4171/ZAA/1211