Divergence of combinatorial averages and the unboundedness of the trilinear Hilbert transform

Abstract

We consider multilinear averages in ergodic theory and harmonic analysis and prove their divergence in some range of $L^p$ spaces, with $p$ close enough to 1. We also prove that the trilinear Hilbert transform is unbounded in a similar range of $L^p$ spaces.

12 pages, 0 figures