论文标题
$ l^{p} $ - $ l^{q} $在$ \ mathbb {r}^d $的基本域上的傅立叶乘数有界数
$L^{p}$-$L^{q}$ boundedness of Fourier multipliers on Fundamental domains of Lattices in $\mathbb{R}^d$
论文作者
论文摘要
在本文中，我们研究了$ l^{p} $ - $ l^{q} $在经典的hörmander条件下的$ \ mathbb {r}^{d} $ $ 1 <p，q <\ iffty $下的fourier乘数的界限。首先，我们在晶格上介绍傅立叶分析，并查看可能的概括。然后，我们证明了Hausdorff-Young的不平等，Paley的不平等和Hausdorff-Young-Paley在Lattices的情况下。这相当于$ l^{p} $ - $ l^{q} $的定量版本的傅立叶乘数。此外，Paley的不平等使我们能够证明耐铁的小木不平等。
In this paper we study the $L^{p}$-$L^{q}$ boundedness of Fourier multipliers on the fundamental domain of a lattice in $\mathbb{R}^{d}$ for $1 < p,q < \infty$ under the classical Hörmander condition. First, we introduce Fourier analysis on lattices and have a look at possible generalisations. We then prove the Hausdorff-Young inequality, Paley's inequality and the Hausdorff-Young-Paley inequality in the context of lattices. This amounts to a quantitative version of the $L^{p}$-$L^{q}$ boundedness of Fourier multipliers. Moreover, the Paley inequality allows us to prove the Hardy-Littlewood inequality.
