Cancellation for the simplex Hilbert transform

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.

8 pages

References in corpus (3)

• Norm convergence of multiple ergodic averages on amenable groups
• Dyadic triangular Hilbert transform of two general and one not too general function
• Cancellation for the multilinear Hilbert transform

Cited by in corpus (9)

• Some Problems in Harmonic Analysis
• Norm-variation of ergodic averages with respect to two commuting transformations
• On side lengths of corners in positive density subsets of the Euclidean space
• Trilinear smoothing inequalities and a variant of the triangular Hilbert transform
• Power-type cancellation for the simplex Hilbert transform
• Singular Brascamp-Lieb inequalities with cubical structure
• A Szemerédi-type theorem for subsets of the unit cube
• Density theorems for anisotropic point configurations
• Modulation invariant operators