Sharpening a theorem of Forelli
Volume 123 / 2019
Annales Polonici Mathematici 123 (2019), 197-201
MSC: 32A10, 32A05.
DOI: 10.4064/ap180616-3-9
Published online: 17 September 2018
Abstract
We prove that a complex-valued function defined on the unit ball in $\mathbb {C}^n$ is holomorphic if and only if it is holomorphic along every complex vector line and satisfies a weak differentiability condition on some real vector planes. We thereby sharpen a classical theorem by Forelli.
