Modulation spaces $M_{p,q}^s$ were introduced by Feichtinger [11] in 1983. Bényi and Oh [2] 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 Bényi and Oh's modulation spaces, we introduce the scaling limit versions of modulation spaces, which contains 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 nonlinear Schrödinger equation in some scaling limit of modulation spaces, which generalize the well posedness results of [3] and [23], and certain super-critical initial data in $H^s$ or in $L^p$ are involved in these spaces.

调制空间 ${\mathrm{中号}}_{p，q}^s$由Feichtinger [11]在1983年提出。Bényi和Oh [2]为Feichtinger的调制空间定义了一个修改版本，为此，对称缩放因其在PDE中的可能应用而被强调。通过仔细研究调制空间的缩放特性及其与Bényi和Oh的调制空间的联系，我们介绍了调制空间的缩放极限版本，其中既包含Feichtinger's和Bényi以及Oh的调制空间。作为它们的应用，我们将在调制空间的某些缩放极限下给出非线性薛定ding方程的局部适定性和（小数据）全局适定性结果，这些结果将概括[3]和[23]的适定性结果，和某些超临界初始数据$H^s$ 或在 ${\mathrm{大号}}^p$ 涉及这些空间。