Mathematical Research Letters
Volume 24 (2017)
Cancellation for the simplex Hilbert transform
Pages: 581 – 592
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.
Received 4 August 2015
Accepted 24 February 2016
Published 24 July 2017