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

Published online by Cambridge University Press:  01 October 2008

CIPRIAN DEMETER
CIPRIAN DEMETER*
Affiliation:
Department of Mathematics, UCLA, Los Angeles CA 90095-1555, USA (email: demeter@math.ias.edu)
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Abstract

We consider multilinear averages in ergodic theory and harmonic analysis and prove their divergence in some range of Lp spaces. This contrasts with the positive behavior exhibited by these averages in a different range, as proved in Demeter et al [Maximal multilinear operators. Trans. Amer. Math. Soc.360(9) (2008), 4989–5042]. We also prove that the trilinear Hilbert transform is unbounded in a similar range of Lp spaces. The principle underlying these constructions is stated, setting the stage for more general results.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 5 , October 2008 , pp. 1453 - 1464
Copyright
Copyright © 2008 Cambridge University Press

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