Chang, Der-Chen; Stević, Stevo Addendum to the paper “A note on weighted Bergman spaces and the Cesàro operator”. (English) Zbl 1090.32500 Nagoya Math. J. 180, 77-90 (2005). Summary: Let \(H({\mathbb D}_n)\) be the space of holomorphic functions on the unit polydisk \({\mathbb D}_n\), and let \({\mathcal L}_\alpha^{p,q}({\mathbb D}_n)\), where \(p,q>0\), \(\alpha=(\alpha_1,\dots,\alpha_n)\) with \(\alpha_j>-1\), \(j=1,\dots,n\), be the class of all measurable functions \(f\) defined on \({\mathbb D}_n\) such that \[ \int_{[0, 1)^n}M^q_p(f,r)\prod^n_{j=1}(1-r_j)^{\alpha_j}dr_j<\infty, \] where \(M_p(f,r)\) denote the \(p\)-integral means of the function \(f\). Denote the weighted Bergman space on \({\mathbb D}_n\) by \({\mathcal A}_\alpha^{p,q}({\mathbb D}_n)\cap H({\mathbb D}_n)\).We provide a characterization for a function \(f\) being in \({\mathcal A}_\alpha^{p,q}({\mathbb D}_n)\). Using the characterization we prove the following result: Let \(p>1\), then the Cesàro operator is bounded on the space \({\mathcal A}_\alpha^{p,p}({\mathbb D})\).[For the original paper see G. Benke and D.-C. Chang, Nagoya Math. J. 159, 25–43 (2000; Zbl 0981.32001)]. Cited in 11 Documents MSC: 32A17 Special families of functions of several complex variables 32A36 Bergman spaces of functions in several complex variables Citations:Zbl 0981.32001 PDFBibTeX XMLCite \textit{D.-C. Chang} and \textit{S. Stević}, Nagoya Math. J. 180, 77--90 (2005; Zbl 1090.32500) Full Text: DOI References: [1] Nagoya Math. J. 159 pp 25– (2000) · Zbl 0981.32001 · doi:10.1017/S0027763000007406 [2] Houston J. Math. 30 pp 511– (2004) [3] Acta Sci. Math. 69 pp 109– (2003) [4] DOI: 10.1080/02781070310001650047 · Zbl 1053.47020 · doi:10.1080/02781070310001650047 [5] Studia Sci. Math. Hung. 39 pp 87– (2002) [6] Acta Sci. Math. 66 pp 651– (2000) [7] DOI: 10.1080/02781070290032216 · Zbl 1027.32005 · doi:10.1080/02781070290032216 [8] Math. Nachr. 248 pp 185– (2003) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.