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Harmonic analysis of several complex variables: a survey. (English) Zbl 1279.32005

Summary: We treat basic issues of harmonic analysis in several complex variables. This includes the study of Hardy spaces, singular integrals, reproducing kernels, partial differential equations, and Fourier analysis. Along the way we indicate several new results in different aspects of the subject.

MSC:

32A50 Harmonic analysis of several complex variables
32A10 Holomorphic functions of several complex variables
32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
32A26 Integral representations, constructed kernels (e.g., Cauchy, Fantappiè-type kernels)
32A30 Other generalizations of function theory of one complex variable
32A35 \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables
32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
32A40 Boundary behavior of holomorphic functions of several complex variables
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