Weighted restriction estimates and application to Falconer distance set problem
By Xiumin Du, Larry Guth, Yumeng Ou, Hong Wang, Bobby Wilson, Ruixiang Zhang. American Journal of Mathematics, 2018
92 citations recorded by the source corpus.
abstract:We prove some weighted Fourier restriction estimates using polynomial partitioning and refined Strichartz estimates. As application we obtain improved spherical average decay rates of the Fourier transform of fractal measures, and therefore improve the results for the Falconer distance set conjecture in three and higher dimensions.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/bb8cd16b54022ec6efc8a79861a052381c020202
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In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- An L2-identity and pinned distance problem (2018, methodology): “Shortly after this paper came out, (1.3) was improved by DuGuth-Ou-Wang-Wilson-Zhang ([7]) when d ≥ 3 and later furthur improved by Du and Zhang ([6]) when d ≥ 4.”
- Sharp L2 estimates of the Schrödinger maximal function in higher dimensions (2018, methodology): “In the case d ≥ 4, this improves the previous best known result in [14]: Theorem 2.”
- An improved result for Falconer’s distance set problem in even dimensions (2020, result): “This is also precisely the route taken in many prior works including [21, 5, 3, 4].”
- On Falconer’s distance set problem in the plane (2018, methodology): “‚ TPW }f T}2 Lp 1{2 : Corollary 4.3 is the result we will actually use in our estimates about the Falconer problem. Theorem 4.2 is closely related to the rened Strichartz estimates from [5], [6] and [7], and we record a corollary in a similar form. To set up the statement, we need to set up a little”