A guide to Carleson's theorem

DOI10.1216/RMJ-2015-45-1-169zbMath1400.42004arXiv1210.0886OpenAlexW2963916045MaRDI QIDQ2340840

Ciprian Demeter

Publication date: 21 April 2015

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.0886

zbMATH Keywords

singular integralsFourier seriesCarleson's theorem

Mathematics Subject Classification ID

Convergence and absolute convergence of Fourier and trigonometric series (42A20) Multipliers in one variable harmonic analysis (42A45)

Related Items (9)

The Failure of the Fractal Uncertainty Principle for the Walsh–Fourier Transform ⋮ DYADIC TRIANGULAR HILBERT TRANSFORM OF TWO GENERAL FUNCTIONS AND ONE NOT TOO GENERAL FUNCTION ⋮ An analogy of the Carleson-Hunt theorem with respect to Vilenkin systems ⋮ Some weak type inequalities and almost everywhere convergence of Vilenkin-Nörlund means ⋮ Variational Carleson operators in UMD spaces ⋮ Pointwise convergence of the non-linear Fourier transform ⋮ Lacunary Fourier and Walsh-Fourier series near \(L^1\) ⋮ Maximal polynomial modulations of singular integrals ⋮ Cesàro summability and Lebesgue points of higher dimensional Fourier series

Cites Work

• Unnamed Item
• Single annulus \(L^p\) estimates for Hilbert transforms along vector fields
• Logarithmic \(L^p\) bounds for maximal directional singular integrals in the plane
• On limits of sequences of operators
• The spaces \(L^ p\), with mixed norm
• Breaking the duality in the return times theorem
• The (weak-\(L^{2}\)) boundedness of the quadratic Carleson operator
• \(L^p\) estimates on the bilinear Hilbert transform for \(2<p<\infty\)
• A proof of boundedness of the Carleson operator
• Carleson's theorem: proof, complements, variations
• \(L^p\) estimates for the Hilbert transforms along a one-variable vector field
• On convergence and growth of partial sums of Fourier series
• Singular integrals along 𝑁 directions in ℝ²
• On the two-dimensional bilinear Hilbert transform
• On a conjecture of E. M. Stein on the Hilbert transform on vector fields
• The quartile operator and pointwise convergence of Walsh series
• A Carleson type theorem for a Cantor group model of the scattering transform
• Maximal theorems for the directional Hilbert transform on the plane
• Sur la convergence presque partout des séries de Fourier-Walsh des fonctions de l'espace L²(0,1)
• Pointwise convergence of Fourier series

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