Pith. sign in

REVIEW 5 cited by

Restriction estimates using decoupling theorems and two-ends Furstenberg inequalities

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2411.08871 v3 pith:HKRQUDHF submitted 2024-11-13 math.CA math.COmath.MG

Hong Wang , Shukun Wu This is my paper · ORCID
classification math.CAmath.COmath.MG
keywords conjecturerestrictionfurstenbergtwo-endsdecouplingdimensionsestimateimplies
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We propose to study the restriction conjecture using decoupling theorems and two-ends Furstenberg inequalities. Specifically, we pose a two-ends Furstenberg conjecture, which implies the restriction conjecture. As evidence, we prove this conjecture in the plane by using the Furstenberg set estimate. Moreover, we use this planar result to prove a restriction estimate for $p>22/7$ in three dimensions, which implies Wolff's $5/2$-hairbrush bound for Kakeya sets in $\mathbb{R}^3$. Our approach also makes improvements for the restriction conjecture in higher dimensions.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Weighted $L^2$ estimates with applications to $L^p$ problems

    math.CA 2025-06 conditional novelty 8.0 of 10

    New weighted L2 estimates with exponent 2/9 for broad Fourier extension operators on 1D fractals yield improvements to maximal Schrodinger, maximal extension, circular Lp decay, and an Lp Mizohata-Takeuchi inequality.

  2. Furstenberg set theorem for transversal families of functions

    math.CA 2025-08 conditional novelty 7.0 of 10

    A sharp dimension bound for Furstenberg sets built from transversal families of graphs, with an application to Fourier decay of fractal measures on convex curves.

  3. Two-ends Furstenberg inequality for transversal families and applications to Fourier decay

    math.CA 2026-07 accept novelty 6.5 of 10

    A simplified two-ends Furstenberg inequality holds for transversal curve families and yields L6 Fourier decay R^{2-5s/2+ε} for s-Frostman measures on convex curves when s≤2/3.

  4. Knapp-type obstructions in multilinear fractal Fourier extension

    math.CA 2026-02 conditional novelty 6.0 of 10

    Multilinear fractal Fourier extension estimates hold when the convolved measures have an L^p density, and fail outside a new, more restrictive range built from Knapp-type examples with linearly independent arithmetic ...

  5. A Survey of the Kakeya conjecture, 2000-2025

    math.CA 2025-12 conditional novelty 2.0 of 10

    An authoritative survey of the Kakeya conjecture (2000–2025), organized around the recent proof that Besicovitch sets in R^3 have full Hausdorff and Minkowski dimension 3.

Pith tools