A Note on the Cone Multiplier

DOI10.2307/2159709zbMath0771.42006OpenAlexW4235818713MaRDI QIDQ4032513

Gerd Mockenhaupt

Publication date: 1 April 1993

Full work available at URL: https://doi.org/10.2307/2159709

zbMATH Keywords

Fourier transformsingular integralconvolution operatorFourier multiplierRiesz meancone multiplier

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Multipliers for harmonic analysis in several variables (42B15)

Related Items (17)

Restriction and Kakeya phenomena for finite fields ⋮ An endline bilinear cone restriction estimate for mixed norms ⋮ A sharp square function estimate for the cone in \(\mathbb{R}^3\) ⋮ On the cone multiplier in \(\mathbb R^3\) ⋮ An endpoint estimate for the cone multiplier ⋮ Estimates for the kinetic transport equation in hyperbolic Sobolev spaces ⋮ Riesz means associated with certain product type convex domain ⋮ Local smoothing estimates for some half-wave operators ⋮ Restriction estimates for some surfaces with vanishing curvatures ⋮ Weak type estimates on certain Hardy spaces for smooth cone type multipliers ⋮ Estimates for cone multipliers associated with homogeneous functions ⋮ Endpoint estimates for bilinear oscillatory integral operators related to restriction to the cone ⋮ A Bochner-Riesz result for a cone ⋮ On Fourier Multipliers Over Tube Domains ⋮ \(L^p\)-\(L^q\) local smoothing estimates for the wave equation via \(k\)-broad Fourier restriction ⋮ Bochner-Riesz means with respect to a rough distance function ⋮ Weak type estimates for cone multipliers on 𝐻^{𝑝} spaces, 𝑝<1

Cites Work

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• Le comportement à l'infini des fonctions de Bessel généralisées. I. (The behaviour at infinity of generalized Bessel functions.)
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• On the convergence of Riesz means on compact manifolds
• Maximal operators related to the Radon transform and the Calderon-Zygmund method of rotations
• The weak type \(L^ 1\) convergence of eigenfunction expansions for pseudodifferential operators
• Inequalities for strongly singular convolution operators
• Oscillatory integrals and multipliers on FL\(^p\)
• A note on spherical summation multipliers
• On Almost Everywhere Convergence of Bochner-Riesz Means in Higher Dimensions
• Oscillatory integrals and multiplier problem for the disc
• Fourier multipliers and estimates of the Fourier transform of measures carried by smooth curves in R²

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