Variational bounds for a dyadic model of the bilinear Hilbert transform

zbMath1304.42033arXiv1203.5135MaRDI QIDQ2509816

Richard Oberlin, Eyvindur Ari Palsson, Yen Do

Publication date: 30 July 2014

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.5135

zbMATH Keywords

variational boundsbilinear Hilbert transformlacunary trees

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Other transformations of harmonic type (42C20)

Related Items (3)

A variation norm Carleson theorem for vector-valued Walsh-Fourier series ⋮ Generalized Carleson embeddings into weighted outer measure spaces ⋮ Singular Brascamp–Lieb: A Survey

Cites Work

• Bounds on the Walsh model for \(M^{q,\ast}\) Carleson and related operators
• Estimates for the square variation of partial sums of Fourier series and their rearrangements
• Pointwise ergodic theorems for arithmetic sets. With an appendix on return-time sequences, jointly with Harry Furstenberg, Yitzhak Katznelson and Donald S. Ornstein
• \(L^p\) estimates for the biest. I: The Walsh case
• The bilinear maximal functions map into \(L^p\) for \(2/3 < p \leq 1\)
• A Calderón Zygmund decomposition for multiple frequencies and an application to an extension of a lemma of Bourgain
• Multi-linear operators given by singular multipliers
• La variation d'ordre p des semi-martingales
• The maximal quartile operator

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