Author:
Benke George,Chang Der-Chen
Abstract
Let B denote the unit ball in ℂn, and dV(z) normalized Lebesgue measure on B. For α > -1, define dVα(z) = (1 - \z\2)αdV(z). Let (B) denote the space of holomorhic functions on B, and for 0 < p < ∞, let p(dVα) denote Lp(dVα) ∩ (B). In this note we characterize p(dVα) as those functions in (B) whose images under the action of a certain set of differential operators lie in Lp(dVα). This is valid for 1 < p < oo. We also show that the Cesàro operator is bounded on p(dVα) for 0 < p < oo. Analogous results are given for the polydisc.
Publisher
Cambridge University Press (CUP)
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