Littlewood-Paley 理论在多参数调和分析中的应用

局部hardy空间在偏微分方程中有着重要的应用。本项目将利用多参数局部再生公式研究多参数局部hardy空间，内容主要包括：多参数局部hardy空间基本理论的建立；多参数拟微分算子在多参数局部hardy空间上的有界性；发展多参数局部Triebel-Lizorkin 空间理论。

Local hardy space has important applications in partial differential equations. The main purpose of this proposal is to study multi-parameter local hardy spaces via multi-parameter local reproducing formula. We will consider the following three problems: the establishment of the theory of multi-parameter local hardy spaces, the boundedness of multi-parameter pseudodifferential operators on multi-parameter local hardy spaces and the development of the theory of multi-parameter local Triebel-Lizorkin spaces.