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

2007/12/15 by Demeter, Ciprian
#Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.0712.2494

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.

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