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Sharpening a theorem of Forelli

Volume 123 / 2019

Jacek Bochnak, Wojciech Kucharz Annales Polonici Mathematici 123 (2019), 197-201 MSC: 32A10, 32A05. DOI: 10.4064/ap180616-3-9 Published online: 17 September 2018


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.


  • Jacek BochnakLe Pont de l’Étang 8
    1323 Romainmôtier, Switzerland
  • Wojciech KucharzInstitute of Mathematics
    Faculty of Mathematics and Computer Science
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland

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