Authors: Chang, Der Chen
Stević, Stevo 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Addendum to the paper "a note on weighted Bergman spaces and the Cesàro operator"
Journal: Nagoya Mathematical Journal
Volume: 180
First page: 77
Last page: 90
Issue Date: 1-Dec-2005
Rank: M21
ISSN: 0027-7630
DOI: 10.1017/S0027763000009193
Abstract: 
Let H(Dn) be the space of holomorphic functions on the unit polydisk Dn, and let script L signαp,q(Dn), where p,q > 0, α = (α1. .., αnwith αj > -1, j = 1,...,n, be the class of all measurable functions f defined on Dn such that ∫(0,1)nMpq(f, r) Πj=1n (1-rj)αj drj < ∞ where Mp(f,r) denote the p-integral means of the function f. Denote the weighted Bergman space on Dn by Aαp,q(Dn) = Lαp,q(D n)∩H(Dn). We provide a characterization for a function f being in Aαp,q(Dn). Using the characterization we prove the following result: Let p > 1, then the Cesàro operator is bounded on the space Aαp,p(Dn).
Publisher: Cambridge University Press
Project: U.S.Department of Defense, Grant DAAH-0496-10301

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