JournalszaaVol. 23, No. 3pp. 577–587

Weighted Integrals of Holomorphic Functions on the Polydisc

  • Stevo Stevic

    Serbian Academy of Science, Beograd, Serbia
Weighted Integrals of Holomorphic Functions on the Polydisc cover
Download PDF

Abstract

We show that a holomorphic function on the unit polydisc UnU^n in Cn{\bf C}^n belongs to the weighted Bergman space Aαp(Un){\cal A}^p_{\alpha}(U^n), when p(0,1],p\in (0,1], if and only if all weighted derivations of order k|k| (with positive orders of derivations) belong to the related weighted Lebesgue space Lαp(Un).{\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.

Cite this article

Stevo Stevic, Weighted Integrals of Holomorphic Functions on the Polydisc. Z. Anal. Anwend. 23 (2004), no. 3, pp. 577–587

DOI 10.4171/ZAA/1211