A bilinear approach to the restriction and Kakeya conjectures

DOI10.1090/S0894-0347-98-00278-1zbMath0924.42008arXivmath/9807163OpenAlexW2157615867WikidataQ123124739 ScholiaQ123124739MaRDI QIDQ4211065

Luis Vega, Ana M. Vargas, Terence C. Tao

Publication date: 10 September 1998

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

Full work available at URL: https://arxiv.org/abs/math/9807163

zbMATH Keywords

bilinear estimatesrestriction theoremKakeya problemdiscretized \(X\)-ray transform

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(L^p\) estimates for the X-ray transform
• Self-spreading and strength of singularities for solutions to semilinear wave equations
• Besicovitch type maximal operators and applications to Fourier analysis
• A geometric inequality with applications to the Kakeya problem in three dimensions
• A mixed norm estimate for the \(X\)-ray transform
• On the regularity properties of a model problem related to wave maps
• A remark on Schrödinger operators
• An improved bound for Kakeya type maximal functions
• A geometric proof of the circular maximal theorem
• The Bochner-Riesz conjecture implies the restriction conjecture
• Restriction theorems and maximal operators related to oscillatory integrals in \(\mathbf R^3\)
• Inequalities for strongly singular convolution operators
• Fourier integral operators. I
• The multiplier problem for the ball
• The Kakeya Maximal Function and the Spherical Summation Multipliers
• Concerning Nikodym-type sets in 3-dimensional curved spaces
• Space‐time estimates for null forms and the local existence theorem
• Oscillatory integrals and multiplier problem for the disc
• A generalization of Bourgain’s circular maximal theorem
• A restriction theorem for the Fourier transform