不规则混合齐次超曲面测度的 Fourier 变换
经典分析与常微分方程
2017-11-15 v4
摘要
借助 Van der Corput 引理，证明了具有可能极不规则密度的混合齐次超曲面测度的 Fourier 变换的衰减估计。主要结果本质上是局部的，但在适当意义上可以推广为全局定理。对于定理中特定范围的指数，这些估计是尖锐的。
引用
@article{arxiv.1409.4059,
title = {Fourier transforms of irregular mixed homogeneous hypersurface measures},
author = {Michael Greenblatt},
journal= {arXiv preprint arXiv:1409.4059},
year = {2017}
}
备注
18 pages. v4: This is essentially the n-dimensional portion of the first two versions of this preprint, the published version of which will soon appear in Math. Nachrichten. The author has recently found a substantially better approach to the two-dimensional problems treated in the previous versions of this preprint, so the two-dimensional part of the previous versions will remain unpublished