Description of Simple Exceptional Sets in the Unit Ball.

For z ∈ ∂Bⁿ, the boundary of the unit ball in \Bbb {C}^n \ {\rm let} \ \Lambda(2)=\{ \lambda : \vert \lambda \vert \leqslan/math>. If f \in \Bbb{O}(B^n)</math> then we call E(f)=\{ z \in \partial B^n: \int_{\Lambda(z)} \vert f(z) \vert ^2 d\Lambda(z)=\infty \}</math> 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)</math> then there exists a holomorphic function f in the unit ball Bⁿ so that E(f) = E. [ABSTRACT FROM AUTHOR]