IMPROVED BOUNDS FOR RESTRICTED PROJECTION FAMILIES VIA WEIGHTED FOURIER RESTRICTION

被引：3
作者：
Harris, Terence L. J. [1 ,2 ]
机构：
[1] Cornell Univ, Dept Math, Ithaca, NY 14850 USA
[2] Univ Illinois, Dept Math, Chicago, IL 60607 USA
来源：
ANALYSIS & PDE | 2022年 / 15卷 / 07期
基金：
美国国家科学基金会;
关键词：
orthogonal projections; Hausdorff dimension; Fourier transform; HAUSDORFF DIMENSION; SPHERICAL AVERAGES; SMOOTHNESS; TRANSFORMS; SETS;
D O I：
10.2140/apde.2022.15.1655
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is shown that if A⊆R3 is a Borel set of Hausdorff dimension (Formula Presented), then for (Formula Presented) the projection (Formula Presented) of A onto the 2-dimensional plane orthogonal to (Formula Presented) satisfies (Formula Presented). This improves the bounds of Oberlin and Oberlin (J. Geom. Anal. 25:3 (2015), 1476–1491) and of Orponen and Venieri (Int. Math. Res. Not. 2020:19 (2020), 5797–5813) for (Formula Presented). More generally, a weaker lower bound is given for families of planes in R3 parametrised by curves in S2 with nonvanishing geodesic curvature. © 2022 Mathematical Sciences Publishers
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收藏
页码：1655 / 1701
页数：48
相关论文
共 31 条
[1]  
[Anonymous], 1954, Proc. Lond. Math. Soc., DOI DOI 10.1112/PLMS/S3-4.1.257
[2]   The proof of the l2 Decoupling Conjecture [J].
Bourgain, Jean ;
Demeter, Ciprian .
ANNALS OF MATHEMATICS, 2015, 182 (01) :351-389
[3]  
Chen CH, 2018, REAL ANAL EXCH, V43, P347
[4]   Fractal Strichartz estimate for the wave equation [J].
Cho, Chu-Hee ;
Ham, Seheon ;
Lee, Sanghyuk .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2017, 150 :61-75
[5]  
Davies R. O., 1952, INDAG MATH, V14, P488
[6]  
Demeter C, 2020, CAM ST AD M, V184, P1, DOI 10.1017/9781108584401
[7]   Sharp L2 estimates of the Schrodinger maximal function in higher dimensions [J].
Du, Xiumin ;
Zhang, Ruixiang .
ANNALS OF MATHEMATICS, 2019, 189 (03) :837-861
[8]  
Erdogan MB, 2004, MATH RES LETT, V11, P299
[9]   Strong Marstrand theorems and dimensions of sets formed by subsets of hyperplanes [J].
Falconer, Kenneth ;
Mattila, Pertti .
JOURNAL OF FRACTAL GEOMETRY, 2016, 3 (04) :319-329
[10]   On restricted families of projections in R3 [J].
Fassler, Katrin ;
Orponen, Tuomas .
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2014, 109 :353-381
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