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A small boundary for \(H^{\infty}\) on a strictly pseudoconvex domain. (English) Zbl 0594.32018
The main theorem shows that if \(D\subset \subset {\mathbb{C}}^ n\) (n\(\geq 2)\) is a strictly pseudoconvex domain with \(C^ k\) boundary bD for \(k>2\), it is indeed possible to construct a closed nowhere dense subset of the maximal ideal space of \(L^{\infty}(bD)\) which defines a closed boundary for \(H^{\infty}(D).\)
Reviewer: Z.Binderman
MSC:
32A38 Algebras of holomorphic functions of several complex variables
32A35 \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables
32T99 Pseudoconvex domains
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