A note on weighted Bergman spaces and the Cesàro operator. (English) Zbl 0981.32001

Let \(A^p(dV_{\alpha})\) denote the set of the functions holomorphic in the unit ball in \(\mathbb{C}^n\), which belong to \(L^p(dV_{\alpha})\) where \(\alpha >-1\), \(0<p<\infty\) and \( dV_{\alpha}={(1-|z|^2)}^{\alpha} dV(z)\). In this paper \(A^p(dV_{\alpha})\) is characterized as those functions whose images under the action of a certain set of differential operators lie in \(L^p(dV_{\alpha})\). It is shown also that the Cesàro operator is bounded on \(A^p(dV_{\alpha})\).


32A17 Special families of functions of several complex variables
32A36 Bergman spaces of functions in several complex variables
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