Real Analysis Exchange

Linear truncations of the Hilbert transform

Loukas Grafakos

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We study \(L^p\) to \(L^q\) mapping properties of nonconvolution singular integral operators on \(\mathbb{R}^1\), whose kernels are obtained by truncating the Hilbert kernel \(1/x\) in ways that depend linearly on the input variable. Some of these operators arise as special cases of the bilinear Hilbert transform and they are shown to map \(L^p\) to \(L^q\) for \(q \lt p\).

Article information

Real Anal. Exchange, Volume 22, Number 1 (1996), 413-427.

First available in Project Euclid: 1 June 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Hilbert transform linear truncations


Grafakos, Loukas. Linear truncations of the Hilbert transform. Real Anal. Exchange 22 (1996), no. 1, 413--427.

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