Geodesic
Exceptional Sets of Slices for Functions From the Bergman Space in the Ball
Canadian mathematical bulletin, Tome 44 (2001) no. 2, pp. 150-159

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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 $E\left( {{B}_{N}},\,f \right)$ 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.
DOI : 10.4153/CMB-2001-019-7
Mots-clés : 32A37, 32A22 
Jakóbczak, Piotr. Exceptional Sets of Slices for Functions From the Bergman Space in the Ball. Canadian mathematical bulletin, Tome 44 (2001) no. 2, pp. 150-159. doi: 10.4153/CMB-2001-019-7
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     title = {Exceptional {Sets} of {Slices} for {Functions} {From} the {Bergman} {Space} in the {Ball}},
     journal = {Canadian mathematical bulletin},
     pages = {150--159},
     year = {2001},
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     doi = {10.4153/CMB-2001-019-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2001-019-7/}
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