\(L^2\)-boundedness of Hilbert transforms along variable curves
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Publication:448243
DOI10.1016/j.jmaa.2012.05.064zbMath1298.44005OpenAlexW2018310970MaRDI QIDQ448243
Publication date: 30 August 2012
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.05.064
Function spaces arising in harmonic analysis (42B35) Special integral transforms (Legendre, Hilbert, etc.) (44A15)
Related Items (7)
\(L^p\) 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 ⋮ Weak (1,1) boundedness of oscillatory singular integral with variable phase ⋮ \(L^2\) 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
Cites Work
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- Hilbert transforms for convex curves
- 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. I
- Hilbert transforms and maximal functions along variable flat plane curves
- Maximal functions and Hilbert transforms along variable flat curves
- Classes of singular integral operators along variable lines
- \(L^ 2\)-estimates for a class of singular oscillatory integrals
- Hilbert transforms and maximal functions along variable flat curves
- Problems in harmonic analysis related to curvature
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