Real Analysis Exchange

Linear truncations of the Hilbert transform

Loukas Grafakos

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Abstract

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

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

Dates
First available in Project Euclid: 1 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1338515235

Mathematical Reviews number (MathSciNet)
MR1433628

Zentralblatt MATH identifier
0879.42009

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

Keywords
Hilbert transform linear truncations

Citation

Grafakos, Loukas. Linear truncations of the Hilbert transform. Real Anal. Exchange 22 (1996), no. 1, 413--427. https://projecteuclid.org/euclid.rae/1338515235


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References

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