Real Analysis Exchange

On Exceptional Sets of the Hilbert Transform

Grigori A. Karagulyan

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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.

Article information

Real Anal. Exchange, Volume 42, Number 2 (2017), 311-328.

First available in Project Euclid: 10 May 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B05: Fourier series and coefficients

Hilbert transform exceptional null set divergent Fourier series


Karagulyan, Grigori A. On Exceptional Sets of the Hilbert Transform. Real Anal. Exchange 42 (2017), no. 2, 311--328. doi:10.14321/realanalexch.42.2.0311.

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