论文标题
Ionescu- Wainger乘数定理和Adeles
The Ionescu--Wainger multiplier theorem and the adeles
论文作者
论文摘要
Ionescu-wainger乘数定理为傅立叶乘数运算符建立了良好的$ l^p $界限；它已成为离散谐波分析中不可或缺的工具。我们提供了具有更明确的常数（删除定理先前版本中存在的对数损失）的简化证明，并给出涉及Adelic傅立叶乘数的更一般的变体。我们还建立了一个密切相关的阿德莱克采样定理，该定理表明$ \ ell^p（\ z^d）$ functions with founier变换的功能规范可与$ l^p（\ a_ \ z^d）$ norm the Adelic对方相媲美。
The Ionescu--Wainger multiplier theorem establishes good $L^p$ bounds for Fourier multiplier operators localized to major arcs; it has become an indispensible tool in discrete harmonic analysis. We give a simplified proof of this theorem with more explicit constants (removing logarithmic losses that were present in previous versions of the theorem), and give a more general variant involving adelic Fourier multipliers. We also establish a closely related adelic sampling theorem that shows that $\ell^p(\Z^d)$ norms of functions with Fourier transform supported on major arcs are comparable to the $L^p(\A_\Z^d)$ norm of their adelic counterparts.
