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

DOI10.1017/S0143385707001101zbMath1168.42007arXiv0712.2494OpenAlexW2963471599MaRDI QIDQ3623579

Ciprian Demeter

Publication date: 21 April 2009

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.2494

zbMATH Keywords

Hilbert transformergodic average

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Ergodic theory of linear operators (47A35) Ergodic theorems, spectral theory, Markov operators (37A30) Linear operators on function spaces (general) (47B38)

Related Items (6)

Cancellation for the multilinear Hilbert transform ⋮ Unboundedness of the trilinear Hilbert transform under the critical index ⋮ DYADIC TRIANGULAR HILBERT TRANSFORM OF TWO GENERAL FUNCTIONS AND ONE NOT TOO GENERAL FUNCTION ⋮ The \((L^p,L^q)\) bilinear Hardy-Littlewood function for the tail ⋮ The \((L^1,L^1)\) bilinear Hardy-Littlewood function and Furstenberg averages ⋮ The polynomial Carleson operator

Cites Work

• \(L^p\) estimates on the bilinear Hilbert transform for \(2<p<\infty\)
• Multiple recurrence and almost sure convergence for weakly mixing dynamical systems
• On Calderón's conjecture
• The bilinear maximal functions map into \(L^p\) for \(2/3 < p \leq 1\)
• Universal characteristic factors and Furstenberg averages
• Maximal multilinear operators
• A new proof of Szemerédi's theorem
• On certain elementary trilinear operators

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