\( \ell^2\) Decoupling for certain surfaces of finite type in \(\mathbb{R}^3\)

DOI10.1007/s10114-023-1374-9zbMath1522.42019MaRDI QIDQ6079302

Ji Qiang Zheng, Zhuoran Li

Publication date: 29 September 2023

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

zbMATH Keywords

decoupling inequalityfinite typeinduction on scalesreduction of dimension arguments

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Higher degree equations; Fermat's equation (11D41) Hypersurfaces and algebraic geometry (14J70)

Cites Work

• Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three
• A study guide for the \(l^{2}\) decoupling theorem
• Bounds on oscillatory integral operators based on multilinear estimates
• On the multilinear restriction and Kakeya conjectures
• Local smoothing type estimates on \(L^p\) for large \(p\)
• Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces
• A restriction estimate for a certain surface of finite type in \(\mathbb{R}^3\)
• Decoupling for mixed-homogeneous polynomials in \({\mathbb{R}}^3\)
• A sharp square function estimate for the cone in \(\mathbb{R}^3\)
• Uniform \(l^2\)-decoupling in \(\mathbb{R}^2\) for polynomials
• A sharp \(L^p-L^q\)-Fourier restriction theorem for a conical surface of finite type
• The proof of the \(l^2\) decoupling conjecture
• ℓ² decoupling in ℝ² for curves with vanishing curvature

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