论文标题
部分可观测时空混沌系统的无模型预测
Real-Variable Theory of Hardy Spaces Associated with Generalized Herz Spaces of Rafeiro and Samko
论文作者
论文摘要
这本书致力于探索广义的HERZ空间的特性，并通过一个完全新鲜的视角建立了与本地和全球广义的HERZ空间相关的耐寒空间的完整可实现的理论，这意味着作者将这些广义的HERZ空间视为球球Quasi-Banach功能空间的特殊案例。确切地说，在本书中，作者首先研究了广义HERZ空间的一些基本特性，并获得了换向器的界限和紧凑性。然后，作者介绍了相关的Herz-Hardy空间，当地的Herz-Hardy空间和弱的Herz-Hardy空间，并对这些Herz-Hardy空间进行了完整的真实理论，包括它们的各种最大功能，原子，有限的原子，分子，分子以及各种Littlewood-Pale-Pale-Paley功能表征。作为应用，作者建立了一些重要的操作员的界限，这是由于对这些HERZ-HARDY空间的谐波分析而产生的。最后，还研究了不均匀的Herz-Hardy空间及其完整的实现理论。由于全球HERZ空间的副空间不足，因此与Ball Quasi-Banach功能空间相关的有关Hardy类型空间相关的可实现的特征不适用于与全球通用的HERZ空间相关的Hardy空间，这些空间需要改进现有的概括，并在此书中进行了改进的现有概括，并在此书中进行了更多的预期应用程序。作者还应指出，从新的角度来看，对与球准散型函数空间相关的可实现的可实现理论的结论得到了改进，本书所有获得的结果中的指数都很清晰。此外，本书中的所有结果都是新的，并且从未出版过。
This book is devoted to exploring properties of generalized Herz spaces and establishing a complete real-variable theory of Hardy spaces associated with local and global generalized Herz spaces via a totally fresh perspective which means that the authors view these generalized Herz spaces as special cases of ball quasi-Banach function spaces. To be precise, in this book, the authors first study some basic properties of generalized Herz spaces and obtain boundedness and compactness characterizations of commutators on them. Then the authors introduce the associated Herz-Hardy spaces, local Herz-Hardy spaces, and weak Herz-Hardy spaces, and develop a complete real-variable theory of these Herz-Hardy spaces, including their various maximal function, atomic, finite atomic, molecular as well as various Littlewood-Paley function characterizations. As applications, the authors establish the boundedness of some important operators arising from harmonic analysis on these Herz-Hardy spaces. Finally, the inhomogeneous Herz-Hardy spaces and their complete real-variable theory are also investigated. Due to the deficiency of the associate space of the global Herz space, the known real-variable characterizations about Hardy-type spaces associated with ball quasi-Banach function spaces are not applicable to Hardy spaces associated with global generalized Herz spaces which need an improved generalization of the existing one, done by the authors also in this book and having more additional anticipating applications. The authors should also point out that, with the fresh perspective and the improved conclusions on the real-variable theory of Hardy spaces associated with ball quasi-Banach function spaces, the exponents in all the obtained results of this book are sharp. Moreover, all of these results in this book are new and have never been published before.
