Cohn, William S. Weighted Bergman projections and tangential area integrals. (English) Zbl 0811.32001 Stud. Math. 106, No. 1, 59-76 (1993). Summary: Let \(\Omega\) be a bounded strictly pseudoconvex domain in \(\mathbb{C}^ n\). We find sufficient conditions on a function \(f\) defined on \(\Omega\) in order that the weighted Bergman projection \(P_ s f\) belong to the Hardy-Sobolev space \(H^ p_ k (\partial \Omega)\). The conditions on \(f\) we consider are formulated in terms of tent spaces and complex tangential vector fields. If \(f\) is holomorphic then these conditions are necessary and sufficient in order that \(f\) belong to the Hardy-Sobolev space \(H^ p_ k (\partial \Omega)\). Cited in 7 Documents MSC: 32A10 Holomorphic functions of several complex variables 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 32T99 Pseudoconvex domains Keywords:weighted Bergman projection; Hardy-Sobolev space PDFBibTeX XMLCite \textit{W. S. Cohn}, Stud. Math. 106, No. 1, 59--76 (1993; Zbl 0811.32001) Full Text: DOI EuDML