Cancellation for the simplex Hilbert transform

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)

Received 4 August 2015

Accepted 24 February 2016

Published 24 July 2017