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Extension and restriction of holomorphic functions. (English) Zbl 0881.32005
Summary: Strong pathologies with respect to growth properties can occur for the extension of holomorphic functions from submanifolds \(D'\) of pseudoconvex domains \(D\) to all of \(D\) even in quite simple situations; the spaces \(A^{p}(D'):={\mathcal O}(D')\cap L^{p}(D')\) are, in general, not at all preserved. Also the image of the Hilbert space \(A^{2}(D)\) under the restriction to \(D'\) can have a very strange structure.

MSC:
32D15 Continuation of analytic objects in several complex variables
32T99 Pseudoconvex domains
32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
32A10 Holomorphic functions of several complex variables
32A35 \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables
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References:
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