Restriction implies Bochner–Riesz for paraboloids

DOI10.1017/S0305004100075599zbMath0759.42011MaRDI QIDQ4008589

Anthony Carbery

Publication date: 27 September 1992

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

zbMATH Keywords

Fourier transformFourier multiplierBochner-Riesz problemrestriction problem\(L^ p\)-multipliers

Mathematics Subject Classification ID

Multipliers for harmonic analysis in several variables (42B15)

Related Items

Restriction and Kakeya phenomena for finite fields ⋮ A note on local smoothing estimates for fractional Schrödinger equations ⋮ On the Bochner-Riesz operator in \(\mathbb{R}^3\) ⋮ Factorization in Fourier restriction theory and near extremizers ⋮ On smoothing estimates for Schrödinger equations on product spaces \(\mathbb{T}^m \times \mathbb{R}^n\) ⋮ Note on Nikodym maximal in the variable Lebesgue spaces ⋮ The Bochner-Riesz conjecture implies the restriction conjecture ⋮ Endpoint maximal and smoothing estimates for Schrödinger equations ⋮ A local smoothing estimate for the Schrödinger equation ⋮ Weak version of restriction estimates for spheres and paraboloids in finite fields ⋮ Finite field restriction estimates based on Kakeya maximal operator estimates ⋮ Conjecture and improved extension theorems for paraboloids in the finite field setting ⋮ Bilinear restriction estimates for surfaces with curvatures of different signs

Cites Work

• Besicovitch type maximal operators and applications to Fourier analysis
• \(L^ p\)-estimates for oscillatory integrals in several variables
• Inequalities for strongly singular convolution operators
• Oscillatory integrals and multipliers on FL\(^p\)
• A note on spherical summation multipliers
• A RESONANCE THEOREM AND SERIES IN EIGENFUNCTIONS OF THE LAPLACIAN
• A restriction theorem for the Fourier transform