论文标题
一级H-分布和变体
One-scale H-distributions and variants
论文作者
论文摘要
H测量和半经典（Wigner）度量是在1990年代初引入的，从那时起，他们在涉及$ \ Mathrm {l}^2 $弱收敛序列的问题中发现了许多应用。尽管它们是相似的对象，但它们都不是对方的概括，但它们之间的根本差异是半经典测量的特征长度，而H测量却没有。最近引入了对象，即一个尺度的H测量，它们都概括了两个，因此涵盖了两者的属性。 本文的主要目的是通过构建一个规模的H-分布，一般的H- measures的概括，同时，h-distribitions的h-distribitions，h-mealization n Nothy $ \ n NOINS p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p p，我们还通过Wigner Transform介绍了$ \ Mathrm {l}^p $扩展半经典测量的替代方法，并引入了新型的对象（半经典分布）。此外，我们以相当通用的形式得出本地化原理，适用于具有特征长度的问题以及没有特定特征长度的问题，从而提供了某些应用。
H-measures and semiclassical (Wigner) measures were introduced in earlyn 1990s and since then they have found numerous applications in problems involving $\mathrm{L}^2$ weakly converging sequences. Although they are similar objects, neither of them is a generalisation of the other, the fundamental difference between them being the fact that semiclassical measures have a characteristic length, while H-measures have none. Recently introduced objects, the one-scale H-measures, generalise both of them, thus encompassing properties of both. The main aim of this paper is to fully develop this theory to the $\mathrm{L}^p$ setting, $p\in(1,\infty)$, by constructing one-scale H-distributions, a generalisation of one-scale H-measures and, at the same time, of H-distributions, a generalisation of H-measures to the $\mathrm{L}^p$ setting, without any characteristic length. We also address an alternative approach to $\mathrm{L}^p$ extension of semiclassical measures via the Wigner transform, introducing new type of objects (semiclassical distributions). Furthermore, we derive a localisation principle in a rather general form, suitable for problems with a characteristic length, as well as those without a specific characteristic length, providing some applications.
