论文标题
关于实际线路上的最佳自相关不平等现象
On optimal autocorrelation inequalities on the real line
论文作者
论文摘要
我们本着Barnard和Steinerberger的工作研究自相关的不平等现象。特别是，我们在这些作者先前考虑的一些不平等现象中获得了对尖锐常数的改进，并且在某些特定环境中也证明了这些不平等的极端化。我们的方法包括在傅立叶分析中将有关的不平等与其他经典的尖锐不平等联系起来，例如尖锐的Hausdorff- Young不平等，采用功能分析以及衡量与合适的双重版本有关的问题工具，以识别和识别和强加条件。
We study autocorrelation inequalities, in the spirit of Barnard and Steinerberger's work. In particular, we obtain improvements on the sharp constants in some of the inequalities previously considered by these authors, and also prove existence of extremizers to these inequalities in certain specific settings. Our methods consist of relating the inequalities in question to other classical sharp inequalities in Fourier analysis, such as the sharp Hausdorff--Young inequality, and employing functional analysis as well as measure theory tools in connection to a suitable dual version of the problem to identify and impose conditions on extremizers.
