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Holomorphic functions of fast growth on submanifolds of the domain. (English) Zbl 0932.32002

Let \(D\subset {\mathbb C}^n\) be a pseudoconvex balanced domain. The author constructs holomorphic functions on \(D\) with a fast growth near the boundary of \(D\) along any linear affine sections of \(D\). For example, a function \(f\in O(D)\) is given such that for any positive-dimensional affine subspace \(\Pi\) of \({\mathbb C}^n\) and for any \(p\), \(1\leq p < \infty\), the restriction \(f|_{\Pi\cap D}\) does not belong to \(L^p(D\cap \Pi)\).

MSC:

32A10 Holomorphic functions of several complex variables
32T99 Pseudoconvex domains
32A07 Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010)
32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
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