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Abstract
The main purpose of this article is to present a localization of Forelli's theorem for functions holomorphic along a standard suspension of linear discs. This generalizes one of the main results of [Y.-W. Cho, K.-T. Kim, Functions holomorphic along a pencil of holomorphic discs, J. Geom. Anal. 31 (2021), 10634–10637] and the original Forelli's theorem.
Acknowledgments
The author would like to thank professor Kang-Tae Kim for various helpful discussions, professor Azimbay Sadullaev for his suggestion on a generalization of Theorem 1.2, and Seungjae Lee for helpful comments. The author also wishes to express his deep gratitude to the referees for their valuable comments on the article.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Funding
Most parts of the paper were written while the author was supported by the National Research Foundation of Korea (NRF-4.0019528) at Pohang University of Science and Technology. The paper was completed at Pusan National University where the author is currently supported by the National Research Foundation of Korea (NRF-2018R1C1B3005963, NRF-2021R1A4A1032418).