Mathematische Zeitschrift

, Volume 293, Issue 3–4, pp 1277–1285 | Cite as

Orthogonal testing families and holomorphic extension from the sphere to the ball

  • Luca Baracco
  • Martino FassinaEmail author


Let \(\mathbb {B}^2\) denote the open unit ball in \(\mathbb {C}^2\), and let \(p\in \mathbb {C}^2\)\\(\overline{\mathbb {B}^2}\). We prove that if f is an analytic function on the sphere \(\partial \mathbb {B}^2\) that extends holomorphically in each variable separately and along each complex line through p, then f is the trace of a holomorphic function in the ball.


Analytic discs Holomorphic extension Testing families 

Mathematics Subject Classification

Primary 32V25 Secondary 32V20 32V40 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dipartimento di Matematica Tullio Levi-CivitaUniversità di PadovaPaduaItaly
  2. 2.Department of MathematicsUniversity of IllinoisUrbanaUSA

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