Highly nonintegrable functions in the unit ball (Q1355258)

The author continues his work on the behavior of holomorphic functions on slices. He shows here that for every natural number \(N\), there is a holomorphic function \(f\) on the unit ball \(B\) of \(\mathbb{C}^N\) such that for every nontrivial subspace \(\Pi \subset \mathbb{C}^N\), the restriction \(f|_{\Pi \cap B} \notin {\mathcal L}^2 (\Pi\cap B)\). Extensions of this result are given for domains more general than \(B\), exponents other than \(p=2\), and more general slices \(\Pi\).