Corpus ID: 227119078

A sharp $L^{10}$ decoupling for the twisted cubic

@article{Jung2020AS,
  title={A sharp \$L^\{10\}\$ decoupling for the twisted cubic},
  author={Hongki Jung},
  journal={arXiv: Classical Analysis and ODEs},
  year={2020}
}
  • Hongki Jung
  • Published 2020
  • Mathematics
  • arXiv: Classical Analysis and ODEs
We prove a sharp $l^{10}(L^{10})$ decoupling for the moment curve in $\mathbb{R}^3$. The proof involves a two-step decoupling combined with new incidence estimates for planks, tubes and plates. 

Figures from this paper

On $L^{12}$ square root cancellation for exponential sums associated with nondegenerate curves in ${\mathbb R}^4$
Abstract. We prove sharp L estimates for exponential sums associated with nondegenerate curves in R. We place Bourgain’s seminal result [2] in a larger framework that contains a continuum ofExpand
Restriction of exponential sums to hypersurfaces
We prove moment inequalities for exponential sums with respect to singular measures, whose Fourier decay matches those of curved hypersurfaces. Our emphasis will be on proving estimates that areExpand

References

SHOWING 1-10 OF 16 REFERENCES
The proof of the $l^2$ Decoupling Conjecture
We prove the $l^2$ Decoupling Conjecture for compact hypersurfaces with positive definite second fundamental form and also for the cone. This has a wide range of important consequences. One of themExpand
Sharp decouplings for three dimensional manifolds in $\mathbb{R}^5$
We prove a sharp decoupling for a class of three dimensional manifolds in R.
Decoupling, exponential sums and the Riemann zeta function
We establish a new decoupling inequality for curves in the spirit of [B-D1], [B-D2] which implies a new mean value theorem for certain exponential sums crucial to the Bombieri-Iwaniec method asExpand
Incidence Estimates for Well Spaced Tubes
We prove analogues of the Szemeredi-Trotter theorem and other incidence theorems using $\delta$-tubes in place of straight lines, assuming that the $\delta$-tubes are well-spaced in a strong sense.
Decouplings for curves and hypersurfaces with nonzero Gaussian curvature
We prove two types of results. First we develop the decoupling theory for hypersurfaces with nonzero Gaussian curvature, which extends our earlier work from [4]. As a consequence of this, we obtainExpand
Decoupling inequalities and some mean-value theorems
The purpose of this paper is to present some further applications of the general decoupling theory from [B-D] and [B-D2] to certain diophantine issues. In particular, we consider mean value estimatesExpand
Average decay estimates for Fourier transforms of measures supported on curves
AbstractWe consider Fourier transforms $$\widehat\mu $$ of densities supported on curves in ℝd. We obtain sharp lower and close to sharp upper bounds for the decay rates of $$\widehat\mu $$ as R →Expand
Small cap decoupling inequalities: Bilinear methods
We obtain sharp small cap decoupling inequalities associated to the moment curve for certain range of exponents $p$. Our method is based on the bilinearization argument due to Bourgain andExpand
Sharp decouplings for three dimensional manifolds in R 5
We prove a sharp decoupling for a class of three dimensional manifolds in R.
Fourier Restriction, Decoupling, and Applications
TLDR
This timely text brings the reader from the classical results to state-of-the-art advances in multilinear restriction theory, the Bourgain–Guth induction on scales and the polynomial method. Expand
...
1
2
...