On the Forelli-Rudin construction and weighted Bergman projections. (English) Zbl 0688.32020

Ligocka, Ewa

Stud. Math. 94, No. 3, 257-272 (1989).

The author’s abstract: “We apply the Forelli-Rudin construction to construct the Sobolev spaces of holomorphic functions on some smooth Hartogs domains and the regularity of weighted Bergman projections on weakly regular pseudoconvex domains. We also study the kernels of weighted Bergman projections on strictly pseudoconvex domains.”

Reviewer: E.J.Straube

MSC:

32A25	Integral representations; canonical kernels (Szegő, Bergman, etc.)
32A07	Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010)
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
32A99	Holomorphic functions of several complex variables
46E20	Hilbert spaces of continuous, differentiable or analytic functions
32T99	Pseudoconvex domains

Keywords:

Sobolev spaces of holomorphic functions; smooth Hartogs domains; weighted Bergman projections; pseudoconvex domains