Skip to content
DraconiticResearch
Search Sources API
194,161 studies31 sourcesUpdated 55 min ago
PreprintCC BY-NC-SA 4.0arXiv

Strip Decoupling Inequalities for the Paraboloid in ℝ3

  • Jacob Glidewell
Open at sourcePDFDOICite

Abstract

Large-cap or large-ensemble decoupling inequalities were initially studied by Demeter. These are intimately connected to the reverse square-function conjecture and restriction conjecture in Fourier restriction theory. By strips, we mean a partition of the R−1-neighborhood of the paraboloid into 1× R−1/2× R−1 curved large-caps. In this article, we prove the sharp ℓ2(L10/3) decoupling estimate for strips in ℝ3. We reduce the strip decoupling inequalities to a planar incidence problem, which is dealt with via two-ends Furstenberg incidence estimates. Our method is inspired by Wang--Wu on the restriction conjecture.

Related

  1. S3DNet: Support-Driven Spatial–Semantic Decoupling for Few-Shot Strip-Steel Surface Defect Segmentation
    Ju Zhao, Jingguang Yang, Fengling Lei +4
    MathematicsPeer-reviewedCC BY 4.0General mathematicsCrossref
  2. Weighted decoupling inequalities via fractal bilinear Kakeya estimates
    Robert Schippa
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  3. Solving Quasi-Variational Inequalities Using the Progressive Decoupling of Linkages
    Manoel Jardim, Claudia Sagastizábal, Mikhail Solodov
    arXivPreprintarXiv licenceFull textOptimisation & controlarXiv
  4. A Mizohata--Takeuchi-type estimate for the hyperbolic paraboloid
    Jongchon Kim, Liang Wang
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  5. Oscillatory Integral Operators Along the Paraboloid and Applications
    Jianghao Zhang
    arXivPreprintCC BY-SA 4.0Full textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{glidewell2026strip,
  title = {{Strip Decoupling Inequalities for the Paraboloid in $\mathbbR^3$}},
  author = {Jacob Glidewell},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.01567},
  eprint = {2610.01567},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.01567},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Strip Decoupling Inequalities for the Paraboloid in ℝ^3
AU  - Jacob Glidewell
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.01567
UR  - https://arxiv.org/abs/2610.01567
AB  - Large-cap or large-ensemble decoupling inequalities were initially studied by Demeter. These are intimately connected to the reverse square-function conjecture and restriction conjecture in Fourier restriction theory. By strips, we mean a partition of the R^−1-neighborhood of the paraboloid into 1× R^−1/2× R^−1 curved large-caps. In this article, we prove the sharp ℓ^2(L^10/3) decoupling estimate for strips in ℝ^3. We reduce the strip decoupling inequalities to a planar incidence problem, which is dealt with via two-ends Furstenberg incidence estimates. Our method is inspired by Wang--Wu on the restriction conjecture.
ER  -