Salem sets in local fields, the Fourier restriction phenomenon and the Hausdorff-Young inequality

被引：4

作者：

Papadimitropoulos, Christos ^{[1
]}

机构：

[1] Univ Edinburgh, Maxwell Inst Math Sci, JCMB, Edinburgh EH9 3JZ, Midlothian, Scotland

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2010年 / 259卷 / 01期

关键词：

Local field; Fourier transform; Vector measure; OPTIMAL DOMAINS; INTEGRAL-REPRESENTATIONS; CONVOLUTION-OPERATORS; KERNEL OPERATORS;

D O I：

10.1016/j.jfa.2010.03.017

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish the existence of Salem sets in the ring of integers of any local field and study the Fourier restriction phenomenon on such sets. Optimal extension of the Hausdorff-Young inequality, initially attained for the torus by G. Mockenhaupt and W. Ricker, is also established in the local field setting. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：1 / 27

页数：27

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