Mathematical Research Letters

Volume 24 (2017)

Number 2

Cancellation for the simplex Hilbert transform

Pages: 581 – 592

DOI: http://dx.doi.org/10.4310/MRL.2017.v24.n2.a16

Author

Pavel Zorin-Kranich (Mathematisches Institut, Universität Bonn, Germany)

Abstract

We show that the truncated simplex Hilbert transform enjoys some cancellation in the sense that its norm grows sublinearly in the number of scales retained in the truncation. This extends the recent result by Tao on cancellation for the multilinear Hilbert transform. Our main tool is the Hilbert space regularity lemma due to Gowers, which enables a very short proof.

2010 Mathematics Subject Classification

Primary 42B20. Secondary 47A07.

Full Text (PDF format)

Paper received on 4 August 2015.