$L^p$-boundedness for the Hilbert transform and maximal operator along a class of nonconvex curves

DOI10.1090/S0002-9939-06-08603-5zbMath1136.42013OpenAlexW2050988078MaRDI QIDQ3419982

Neal Bez

Publication date: 1 February 2007

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-06-08603-5

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Multipliers for harmonic analysis in several variables (42B15)

Related Items (7)

Maximal functions along convex curves with lacunary directions ⋮ Oscillatory hyper Hilbert transforms along general curves ⋮ Unnamed Item ⋮ \(L^p\)-estimates for the rough singular integrals associated to surfaces ⋮ \(L^2\) boundedness of Hilbert transforms along variable flat curves ⋮ MAXIMAL OPERATORS AND HILBERT TRANSFORMS ALONG FLAT CURVES NEAR L¹ ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Hilbert transforms for convex curves
• Operators associated to flat plane curves: \(L^ p\) estimates via dilation methods
• Estimates for Wainger's singular integrals along curves
• \(L^ p\)-estimates for operators associated to oscillating plane curves
• Maximal functions and Hilbert transforms associated to polynomials
• The Hilbert transform and maximal function along nonconvex curves in the plane
• Hilbert transforms and maximal functions along rough flat curves
• An oscillatory integral estimate associated to rational phases
• Singular integral and maximal operators associated to hypersurfaces: \(L^p\) theory
• 𝐿^{𝑝} estimates for maximal functions and Hilbert transforms along flat convex curves in 𝐑²
• Differentiation in lacunary directions
• Problems in harmonic analysis related to curvature
• Singular Integrals and Maximal Functions Associated to Surfaces of Revolution

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