## Real Analysis Exchange

### Linear truncations of the Hilbert transform

Loukas Grafakos

#### 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

https://projecteuclid.org/euclid.rae/1338515235

Mathematical Reviews number (MathSciNet)
MR1433628

Zentralblatt MATH identifier
0879.42009

#### 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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