Vector-valued inequalities for families of bilinear Hilbert transforms and applications to bi-parameter problems

DOI10.1112/jlms/jdu044zbMath1311.42021arXiv1203.3251OpenAlexW2168538265MaRDI QIDQ2934791

Prabath Silva

Publication date: 22 December 2014

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.3251

zbMATH Keywords

vector-valued inequalitiesbilinear Hilbert transforms\(L^p\) estimates

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10)

Related Items (8)

A Bilinear Rubio de Francia Inequality for Arbitrary Rectangles ⋮ Extrapolation for multilinear Muckenhoupt classes and applications ⋮ The bilinear Hilbert transform in UMD spaces ⋮ Banach-valued multilinear singular integrals ⋮ Sparse domination via the helicoidal method ⋮ Limited range multilinear extrapolation with applications to the bilinear Hilbert transform ⋮ Banach-valued modulation invariant Carleson embeddings and outer-\(L^p\) spaces: the Walsh case ⋮ Quasi-Banach valued inequalities via the helicoidal method

Cites Work

• Single annulus \(L^p\) estimates for Hilbert transforms along vector fields
• The vector valued quartile operator
• Bi-parameter paraproducts
• The spaces \(L^ p\), with mixed norm
• On Calderón's conjecture
• \(L^p\) estimates for the biest. II: The Fourier case
• \(L^p\) estimates for the Hilbert transforms along a one-variable vector field
• Multi-linear operators given by singular multipliers
• The disc as a bilinear multiplier
• Maximal theorems for the directional Hilbert transform on the plane

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