The quartile operator and pointwise convergence of Walsh series

DOI10.1090/S0002-9947-00-02577-0zbMath0976.42017OpenAlexW1892433509MaRDI QIDQ4508142

Christoph Thiele

Publication date: 3 October 2000

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-00-02577-0

zbMATH Keywords

Walsh functionsconvergence of Fourier seriesbilinear Hilbert transformtime-frequency analysisCarleson's theoremWalsh serieslinear Hilbert transform

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Convergence and absolute convergence of Fourier and trigonometric series (42A20) Conjugate functions, conjugate series, singular integrals (42A50)

Related Items

The Failure of the Fractal Uncertainty Principle for the Walsh–Fourier Transform ⋮ Pointwise convergence of Fourier series. I: On a conjecture of Konyagin ⋮ On weighted norm inequalities for the Carleson and Walsh-Carleson operator ⋮ The vector valued quartile operator ⋮ New exceptional sets and convergence of the square partial sums of Walsh-Fourier series ⋮ Uniform estimates on multi-linear operators with modulation symmetry. ⋮ Weak-\(L^p\) bounds for the Carleson and Walsh-Carleson operators ⋮ Endpoint bounds for the quartile operator ⋮ A uniform estimate for quartile operators ⋮ On geometric and analytic mixing scales: comparability and convergence rates for transport problems ⋮ The Walsh model for \(M_2^*\) Carleson ⋮ Estimates for \(n\)-widths of multiplier operators of multiple Walsh series ⋮ 𝐿^{𝑝} theory for outer measures and two themes of Lennart Carleson united ⋮ A guide to Carleson's theorem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(L^p\) estimates on the bilinear Hilbert transform for \(2<p<\infty\)
• A fast algorithm for adapted time-frequency tilings
• On convergence and growth of partial sums of Fourier series
• An inequality of Paley and convergence a.e. of Walsh-Fourier series
• L ^p estimates for the bilinear Hilbert transform
• A Remarkable Series of Orthogonal Functions (I)
• Sur la convergence presque partout des séries de Fourier-Walsh des fonctions de l'espace L²(0,1)
• A note on the interpolation of linear operations
• Pointwise convergence of Fourier series