Restriction of the Fourier transform to some complex curves

DOI10.1016/j.jmaa.2013.07.073zbMath1308.42005arXiv1111.6409OpenAlexW2963374264MaRDI QIDQ2257776

Jong-Guk Bak, Seheon Ham

Publication date: 2 March 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.6409

zbMATH Keywords

complex curvesaffine arclength measureFourier transforms of measuresFourier restriction problem

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Polynomials and rational functions of one complex variable (30C10)

Related Items (4)

Bilinear restriction estimates for surfaces of codimension bigger than \(1\) ⋮ Uniform convolution estimates for complex polynomial curves in \(\mathbb{C}^3\) ⋮ Convolution estimates for measures on some complex curves ⋮ On the Oberlin affine curvature condition

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Endpoint \(L^p \rightarrow L^q\) bounds for integration along certain polynomial curves
• Restrictions of Fourier transforms to curves
• Universal \(L^p\) improving for averages along polynomial curves in low dimensions
• Maximal functions and Hilbert transforms associated to polynomials
• Affine dimension: measuring the vestiges of curvature.
• Maximal functions and singular integrals associated to polynomial mappings of \(\mathbb R^ n\).
• Trigonometric sums in number theory and analysis. Transl. from the Russian
• Some convolution inequalities and their applications
• Uniform estimates for the local restriction of the Fourier transform to curves
• Degenerate curves and harmonic analysis
• RESTRICTION OF FOURIER TRANSFORMS TO CURVES II: SOME CLASSES WITH VANISHING TORSION
• Fourier restriction to polynomial curves I: a geometric inequality
• Restriction of Fourier transforms to curves and related oscillatory integrals
• On the Restriction of The Fourier Transform to Curves: Endpoint Results and The Degenerate Case
• Fourier restriction theorems for curves with affine and Euclidean arclengths
• Fourier restriction theorems for degenerate curves
• Linear Operators on L p for 0 < p < 1
• Fourier multipliers and estimates of the Fourier transform of measures carried by smooth curves in R²
• Estimates for an oscillatory integral operator related to restriction to space curves
• A note on Restriction of the Fourier Transform to Spheres
• An affine-invariant inequality for rational functions and applications in harmonic analysis
• Some remarks on the restriction of the Fourier transform to surfaces
• Singular integral operators associated to curves with rational components

This page was built for publication: Restriction of the Fourier transform to some complex curves