Weighted Integrals of Holomorphic Functions on the Polydisc II

  • Stevo Stevic

    Serbian Academy of Science, Beograd, Serbia

Abstract

Let denote the class of all measurable functions defined on the unit polydisc such that

where , , and is the normalized area measure on the unit disk , the class of all holomorphic functions on , and let (the weighted Bergman space). In this paper we prove that for if and only if the functions

belong to the space for every where is the characteristic function of is the cardinal number of and where This result extends Theorem 22 of Kehe Zhu in Trans. Amer. Math. Soc. 309 (1988) (1), 253–268, when Also in the case , we present a new proof.

Cite this article

Stevo Stevic, Weighted Integrals of Holomorphic Functions on the Polydisc II. Z. Anal. Anwend. 23 (2004), no. 4, pp. 775–782

DOI 10.4171/ZAA/1222