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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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