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arXiv · 0712.2494

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

Ciprian Demeter
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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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Ciprian Demeter. 2007-12-15. Divergence of combinatorial averages and the unboundedness of the trilinear Hilbert transform. https://arxiv.org/abs/0712.2494

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