Open Access
2017 On Exceptional Sets of the Hilbert Transform
Grigori A. Karagulyan
Real Anal. Exchange 42(2): 311-328 (2017). DOI: 10.14321/realanalexch.42.2.0311


We prove several theorems concerning the exceptional sets of the Hilbert transform on the real line. In particular, it is proved that any null set is an exceptional set for the Hilbert transform of an indicator function. The paper also provides a real variable approach to the Kahane-Katsnelson theorem on divergence of Fourier series.


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Grigori A. Karagulyan. "On Exceptional Sets of the Hilbert Transform." Real Anal. Exchange 42 (2) 311 - 328, 2017.


Published: 2017
First available in Project Euclid: 10 May 2018

zbMATH: 06870332
MathSciNet: MR3721804
Digital Object Identifier: 10.14321/realanalexch.42.2.0311

Primary: 42B05 , 42B20

Keywords: divergent Fourier series , exceptional null set , Hilbert transform

Rights: Copyright © 2017 Michigan State University Press

Vol.42 • No. 2 • 2017
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