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1996/1997 Linear truncations of the Hilbert transform
Loukas Grafakos
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Real Anal. Exchange 22(1): 413-427 (1996/1997).


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 \(q \lt p\).


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Loukas Grafakos. "Linear truncations of the Hilbert transform." Real Anal. Exchange 22 (1) 413 - 427, 1996/1997.


Published: 1996/1997
First available in Project Euclid: 1 June 2012

zbMATH: 0879.42009
MathSciNet: MR1433628

Primary: 42B20

Keywords: Hilbert transform , linear truncations

Rights: Copyright © 1996 Michigan State University Press

Vol.22 • No. 1 • 1996/1997
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