The (weak-\(L^{2}\)) boundedness of the quadratic Carleson operator

DOI10.1007/s00039-009-0010-xzbMath1178.42007arXiv0710.2168OpenAlexW2128582753MaRDI QIDQ1034674

Victor Lie

Publication date: 6 November 2009

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.2168

Mathematics Subject Classification ID

Convergence and absolute convergence of Fourier and trigonometric series (42A20) Conjugate functions, conjugate series, singular integrals (42A50)

Related Items (21)

Pointwise convergence of Fourier series. I: On a conjecture of Konyagin ⋮ DYADIC TRIANGULAR HILBERT TRANSFORM OF TWO GENERAL FUNCTIONS AND ONE NOT TOO GENERAL FUNCTION ⋮ Single annulus estimates for the variation-norm Hilbert transforms along Lipschitz vector fields ⋮ Uniform bounds for oscillatory and polynomial Carleson operators ⋮ Vector valued maximal Carleson type operators on the weighted Lorentz spaces ⋮ Discrete analogues of maximally modulated singular integrals of Stein-Wainger type: \(\ell^p\) bounds for \(p > 1\) ⋮ The polynomial Carleson operator ⋮ A unified approach to three themes in harmonic analysis. I \& II: I. The linear Hilbert transform and maximal operator along variable curves. II Carleson type operators in the presence of curvature ⋮ Maximal polynomial modulations of singular Radon transforms ⋮ Estimates for Hilbert transforms along variable general curves ⋮ Analysis and applications: The mathematical work of Elias Stein ⋮ Sparse Bounds for Random Discrete Carleson Theorems ⋮ The Hilbert transform along the parabola, the polynomial Carleson theorem and oscillatory singular integrals ⋮ Sparse bounds for maximal monomial oscillatory Hilbert transforms ⋮ Polynomial Carleson operators along monomial curves in the plane ⋮ Weak (1,1) boundedness of oscillatory singular integral with variable phase ⋮ Maximal polynomial modulations of singular integrals ⋮ Bounds for anisotropic Carleson operators ⋮ A guide to Carleson's theorem ⋮ Singular Brascamp–Lieb: A Survey ⋮ Oscillatory integrals related to Carleson's theorem: fractional monomials

Cites Work

• On limits of sequences of operators
• \(L^p\) estimates on the bilinear Hilbert transform for \(2<p<\infty\)
• On Calderón's conjecture
• A proof of boundedness of the Carleson operator
• Oscillatory integrals related to Carleson's theorem
• Carleson's theorem: proof, complements, variations
• On convergence and growth of partial sums of Fourier series
• Carleson's theorem with quadratic phase functions
• Pointwise convergence of Fourier series

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