Abstract
For Fatou’s interpolation theorem of 1906 we suggest a new elementary proof.
Similar content being viewed by others
Notes
If \(1 \notin F\), then we assume \(1 \notin G_n\) for all n (this will simplify the proofs).
References
Danielyan, A.A.: A theorem of Lohwater and Piranian. Proc. AMS 144, 3919–3920 (2016)
Danielyan, A.A.: Fatou’s interpolation theorem implies the Rudin-Carleson theorem. J. Fourier Anal. Appl. 23, 656–659 (2017)
Danielyan, A.A.: On Fatou’s theorem. Anal. Math. Phys. 10, 28 (2020)
Fatou, P.: Séries trigonométriques et séries de Taylor. Acta Math. 30, 335–400 (1906)
Garnett, J.B.: Bounded Analytic Functions. Academic Press, Cambridge (1981)
Hoffman, K.: Banach Spaces of Analytic Functions. Prentice Hall, Englewood Cliffs (1962)
Koosis, P.: Introduction to \(H^p\) Spaces. Cambridge University Press, Cambridge (1998)
Privalov, I.I.: Boundary Properties of Analytic Functions, 2nd edn. GITTL, Moscow-Leningrad (1950). (in Russian)
Zygmund, A.: Trigonometric Series, vol. 1. Cambridge University Press, Cambridge (1959)
Acknowledgements
Funding was provided by Simons Foundation (Grant No. 430329).
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Hans G. Feichtinger.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Danielyan, A.A. A Proof of Fatou’s Interpolation Theorem. J Fourier Anal Appl 28, 45 (2022). https://doi.org/10.1007/s00041-022-09936-4
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00041-022-09936-4