Decoupling inequalities for quadratic forms

DOI10.1215/00127094-2022-0033OpenAlexW4315641212MaRDI QIDQ2683550

Ruixiang Zhang, Pavel Zorin-Kranich, Changkeun Oh, Shaoming Guo

Publication date: 13 February 2023

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.09451

zbMATH Keywords

quadratic formBrascamp-Lieb inequalitiesFourier decoupling

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Inequalities for trigonometric functions and polynomials (26D05) Weyl sums (11L15)

Related Items (1)

Fourier decay of fractal measures on surfaces of co-dimension two in \(\mathbb{R}^5\)

Cites Work

• Unnamed Item
• Unnamed Item
• 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
• The endpoint case of the Bennett-Carbery-Tao multilinear Kakeya conjecture
• Bounds on oscillatory integral operators based on multilinear estimates
• Decouplings for three-dimensional surfaces in \(\mathbb{R}^{6}\)
• Kakeya-Brascamp-Lieb inequalities
• Wolff's inequality for hypersurfaces
• On the multilinear restriction and Kakeya conjectures
• On a planar variant of the Kakeya problem
• Decouplings for surfaces in \(\mathbb{R}^4\)
• Hilbert integrals, singular integrals, and Radon transforms. I
• Hilbert integrals, singular integrals, and Radon transforms. II
• Besicovitch type maximal operators and applications to Fourier analysis
• A local smoothing estimate in higher dimensions.
• Local smoothing type estimates on \(L^p\) for large \(p\)
• Restriction estimates using polynomial partitioning. II
• The endpoint perturbed Brascamp-Lieb inequalities with examples
• Decouplings for curves and hypersurfaces with nonzero Gaussian curvature
• Restriction of the Fourier transform to a quadratic surface in \(\mathbb{R}^n\)
• Convolution and restriction estimates for a 3-surface in \(\mathbb{R}^5\)
• The endpoint multilinear Kakeya theorem via the Borsuk-Ulam theorem
• Moment inequalities for trigonometric polynomials with spectrum in curved hypersurfaces
• The Bochner-Riesz conjecture implies the restriction conjecture
• \(L^p\)-improving estimates for Radon-like operators and the Kakeya-Brascamp-Lieb inequality
• An \(l^2\) decoupling interpretation of efficient congruencing: the parabola
• Small cap decouplings. With an appendix by D. R. Heath-Brown.
• Restriction estimates to complex hypersurfaces
• Finite bounds for Hölder-Brascamp-Lieb multilinear inequalities
• Decoupling for moment manifolds associated to Arkhipov-Chubarikov-Karatsuba systems
• On integer solutions of Parsell-Vinogradov systems
• On the Oberlin affine curvature condition
• The proof of the \(l^2\) decoupling conjecture
• Bounds for Kakeya-type maximal operators associated with \(k\)-planes
• Simultaneous integer values of pairs of quadratic forms
• Bilinear restriction estimates for surfaces of codimension bigger than \(1\)
• Sharp bounds for the cubic Parsell-Vinogradov system in two dimensions
• Sharp decouplings for three dimensional manifolds in \(\mathbb{R}^5\)
• The Brascamp-Lieb inequalities: Finiteness, structure and extremals
• Fourier restriction estimates for surfaces of co-dimension two in \(\mathbb{R}^5\)
• Decoupling, exponential sums and the Riemann zeta function
• Mean value estimates for Weyl sums in two dimensions
• On Spaces of Linear Transformations with Bounded Rank
• On plate decompositions of cone multipliers
• On the Restriction of The Fourier Transform to Curves: Endpoint Results and The Degenerate Case
• Stability of the Brascamp-Lieb constant and applications
• Regularized Brascamp–lieb Inequalities and an Application
• The Vinogradov Mean Value Theorem [after Wooley, and Bourgain, Demeter and Guth]
• EFFECTIVE l ² DECOUPLING FOR THE PARABOLA
• Decoupling for certain quadratic surfaces of low co‐dimensions
• Generalized curvature for certain Radon-like operators of intermediate dimension
• A Restriction Theorem for a k-Surface in ℝ_n
• Behaviour of the Brascamp–Lieb constant
• A short proof of the multilinear Kakeya inequality
• Decoupling for two quadratic forms in three variables: a complete characterization

This page was built for publication: Decoupling inequalities for quadratic forms