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Search: MSC category 32A22 ( Nevanlinna theory (local); growth estimates; other inequalities {For geometric theory, see 32H25, 32H30} )

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1. CMB 2001 (vol 44 pp. 150)

Jakóbczak, Piotr
Exceptional Sets of Slices for Functions From the Bergman Space in the Ball
Let $B_N$ be the unit ball in $\mathbb{C}^N$ and let $f$ be a function holomorphic and $L^2$-integrable in $B_N$. Denote by $E(B_N,f)$ the set of all slices of the form $\Pi =L\cap B_N$, where $L$ is a complex one-dimensional subspace of $\mathbb{C}^N$, for which $f|_{\Pi}$ is not $L^2$-integrable (with respect to the Lebesgue measure on $L$). Call this set the exceptional set for $f$. We give a characterization of exceptional sets which are closed in the natural topology of slices.

Categories:32A37, 32A22

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