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Description of Simple Exceptional Sets in the Unit Ball

Author： Kot Piotr

Publisher： Springer Publishing Company

ISSN： 0011-4642

Source： Czechoslovak Mathematical Journal, Vol.54, Iss.1, 2004-03, pp. : 55-63

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

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Abstract

For z ∈ ∂Bⁿ, the boundary of the unit ball in \Bbb {C}^n \ {\rm let} \ \Lambda(2)=\{ \lambda : \vert \lambda \vert \leqslant 1 \}. If $f \in \bbb{o}(b^n)$ then we call $e(f)=\{ z \in \partial b^n: \int_{\lambda(z)} \vert f(z) \vert ^2 d\lambda(z)=\infty \}$ the exceptional set for f. In this note we give a tool for describing such sets. Moreover we prove that if E is a G_δ and f_σ subset of the projective (n − 1)-dimensional space $\bbb{p}^{n-1}=\bbb{p}(\bbb{c}^n)$ then there exists a holomorphic function f in the unit ball Bⁿ so that E(f) = E.

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