Hilbert transforms and maximal functions along variable flat curves

DOI10.1090/S0002-9947-02-03087-8zbMath1017.44003OpenAlexW1587422352MaRDI QIDQ3151258

Jonathan M. Bennett

Publication date: 7 October 2002

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-02-03087-8

zbMATH Keywords

Fourier transformboundednessmaximal functionsHilbert transformsoscillatory singular integralsvariable flat curves

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Radon transform (44A12)

Related Items (11)

\(L^p\) bounds of maximal operators along variable planar curves in the Lipschitz regularity ⋮ 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 ⋮ Estimates for Hilbert transforms along variable general curves ⋮ \(L^2\)-boundedness of Hilbert transforms along variable curves ⋮ Weak (1,1) boundedness of oscillatory singular integral with variable phase ⋮ Oscillatory hyper Hilbert transforms along curves ⋮ \(L^2\) boundedness of Hilbert transforms along variable flat curves ⋮ Hilbert transforms along variable planar curves: Lipschitz regularity ⋮ \(L^p\) boundedness of Carleson \& Hilbert transforms along plane curves with certain curvature constraints ⋮ Oscillatory hyper Hilbert transforms along variable curves ⋮ Singular Radon transforms along odd curves on the Heisenberg group

Cites Work

• Operators associated to flat plane curves: \(L^ p\) estimates via dilation methods
• Harmonic analysis on nilpotent groups and singular integrals. I: Oscillatory integrals
• Hilbert integrals, singular integrals, and Radon transforms. II
• Hilbert transforms and maximal functions along variable flat plane curves
• Maximal functions and Hilbert transforms along variable flat curves
• \(L^ 2\)-estimates for a class of singular oscillatory integrals
• 𝐿^{𝑝} estimates for maximal functions and Hilbert transforms along flat convex curves in 𝐑²
• Hilbert Transforms and Maximal Functions Associated to Flat Curves on the Heisenberg Group

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