\(L^ p\) bounds for Hilbert transforms along convex curves

DOI10.1007/BF01388753zbMath0641.42009MaRDI QIDQ1100674

Stephen Wainger, Alexander Nagel, Antonio Córdoba, James Vance, David A. Weinberg

Publication date: 1986

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143304

zbMATH Keywords

Fourier transformdistributionconvex curveHilbert transform operatorL p-bound

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Conjugate functions, conjugate series, singular integrals (42A50)

Related Items

\(L^p\) bounds of maximal operators along variable planar curves in the Lipschitz regularity ⋮ 𝐿^{𝑝} estimates for maximal functions and Hilbert transforms along flat convex curves in 𝐑² ⋮ Bilinear Hilbert transforms and (sub)bilinear maximal functions along convex curves ⋮ The maximal Hilbert transform along nonconvex curves ⋮ 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 ⋮ \(L^p\)-estimates for the rough singular integrals associated to surfaces ⋮ Hilbert transforms along convex curves for \(l^q\)-valued functions ⋮ Hilbert transforms along variable planar curves: Lipschitz regularity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hilbert transforms for convex curves
• The spaces \(L^ p\), with mixed norm
• The Hilbert Transform for Convex Curves in R n
• The Hilbert Transform and Maximal Function for Approximately Homogeneous Curves
• Singular Integrals and Maximal Functions Associated with Highly Monotone Curves
• Hilbert Transforms Associated With Plane Curves
• On the equivalence between the boundedness of certain classes of maximal and multiplier operators in Fourier analysis
• Differentiation in lacunary directions
• Problems in harmonic analysis related to curvature