论文标题
调制空间及其应用的缩放极限
Scaling limit of Modulation Spaces and Their Applications
论文作者
论文摘要
Feichtinger \ cite \ cite {fei83}在1983年介绍了调制空间$ m^s_ {p，q} $。通过诉诸小波，Bényi和Oh \ cite {beoH20}将修改后的版本定义为Feichtinger的适用范围的改装空间，该版本的适用性为PROPASITIONS PROPASITIONS PROPASIDET PRESSIDECE。通过仔细研究调制空间的缩放属性及其与小波基础的连接，我们将引入一类广义调制空间，其中包含Feichtinger和Bényi和OH的调制空间。作为它们的应用，我们将在某些更粗糙的广义调制空间中给予NLS的本地良好性和（小数据）全球范围的结果，这将概述\ cite {beok09}和\ cite {beok09}和\ cite {wahud07}的良好姿势结果，以及在$ h^s $或$ l l^p $中的某些超级策略初始数据。
Modulation spaces $M^s_{p,q}$ were introduced by Feichtinger \cite{Fei83} in 1983. By resorting to the wavelet basis, Bényi and Oh \cite{BeOh20} defined a modified version to Feichtinger's modulation spaces for which the symmetry scalings are emphasized for its possible applications in PDE. By carefully investigating the scaling properties of modulation spaces and their connections with the wavelet basis, we will introduce a class of generalized modulation spaces, which contain both Feichtinger's and Bényi and Oh's modulation spaces. As their applications, we will give a local well-posedness and a (small data) global well-posedness results for NLS in some rougher generalized modulation spaces, which generalize the well posedness results of \cite{BeOk09} and \cite{WaHud07}, and certain super-critical initial data in $H^s$ or in $L^p$ are involved in these spaces.
