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Weighted Bergman projections on the polydisc. (English) Zbl 0818.32007

The author proves a number of results characterizing the range of the weighted Bergman projection \(P_ \alpha\) on the unit polydisc corresponding to the weight \(\prod_{k=1}^ n (1 - | z_ k |^ 2)^{\alpha_ k}\), where each \(\alpha_ k > - 1\). The main theorem is that \(P_ \alpha\) maps the space \(L^ p\) onto a holomorphic Besov-type space that is independent of \(\alpha\). Applications are given to duality and to Hankel operators.

MSC:

32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
32C37 Duality theorems for analytic spaces
47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
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