Holomorphic functions and integral representations in several complex variables. (English) Zbl 0591.32002

Graduate Texts in Mathematics, 108. New York etc.: Springer-Verlag. XIX, 386 p. DM 128.00 (1986).
The methods of integral representations have invaded successfully the theory of functions of several complex variables in the 1970’s, originating principally with the work of G. M. Henkin. The book under review is a textbook which presents an as elementary as possible exposition of this theory and of its main applications. The main topics covered are: integral representations of Cauchy-Fantappiè type, Levi problem and solution of \({\bar \partial}\) on strictly pseudoconvex domains, integral representations of Henkin-Ramirez and estimates for the \({\bar \partial}\)-problem, boundary regularity of biholomorphic maps. Historical comments and indications on recent developments are given.
Reviewer: G.Roos


32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
32A10 Holomorphic functions of several complex variables
32-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to several complex variables and analytic spaces
32T99 Pseudoconvex domains
32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
32H99 Holomorphic mappings and correspondences