What question did this study set out to answer?

The dissertation aims to explore Fourier restriction and its implications in various mathematical contexts.

December 19, 2025Open Access

Fourier Restriction: From Linear Restriction to Multilinear Restriction

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SZS. ZhangShanghai University of Engineering Science

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Implication

This dissertation explores Fourier restriction in spacial domains and verifies restrictions in the Fourier domain, suggesting deeper insights into the restriction problem.

Key Points

The dissertation aims to explore Fourier restriction and its implications in various mathematical contexts.
Discussion of linear restriction and Hausdorff-Young's inequality.
Proof of restriction estimates on curves and on the sphere/paraboloid via the Stein-Tomas argument.
Investigation of bilinear restriction with a focus on the 2-dimensional case using reverse square function estimates.
Verification of the restriction conjecture on the 2-dimensional paraboloid.
Examination of multilinear restriction estimates and results from I. Bejenaru.
Identified ranges for constants p, q in Fourier restriction cases.
Established bounds for L^q norm in spacial domains relative to L^p norms.
Proved key estimates for bilinear and multilinear restrictions.

Cite This Study

S. Zhang (2025) studied this question.

synapsesocial.com/papers/69449a922f0218eca9508737 https://doi.org/10.48550/arxiv.2512.11888

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Implication

This dissertation explores Fourier restriction in spacial domains and verifies restrictions in the Fourier domain, suggesting deeper insights into the restriction problem.

Fourier Restriction: From Linear Restriction to Multilinear Restriction

Discussion

Member takes

Implication

Key Points

Cite This Study

Fourier Restriction: From Linear Restriction to Multilinear Restriction

Discussion

Member takes

Implication

Key Points

Cite This Study

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