函数空间实变理论及其上的算子有界性是调和分析研究的核心内容之一，已被广泛应用于数学和物理的许多分支. 申请人及其合作者已研究了各种底空间上的Hardy空间实变理论, 包括变指标Hardy空间、(Musielak-)Orlicz-Hardy空间及其相关于算子的变形空间的实变理论. 本课题拟在这些Hardy空间研究基础上, 结合Hardy空间与广泛应用于时频分析的Amalgam空间，系统发展相关于(加权)Amalgam空间的Amalgam-Hardy空间实变理论, 包括原子和分子分解、Riesz变换特征、Littlewood-Paley特征、对偶空间及插值性质等. 在此基础上, 进一步发展更一般的Amalgam型Besov-Triebel-Lizorkin空间，探讨这些空间自身之间及与经典的模空间和Besov-Triebel-Lizorkin空间之间的密切联系, 并将其应用于算子有界性的研究.

The real-variable theory of function spaces and the boundedness of operators on function spaces is one central topic of harmonic analysis, which has been widely used in various branches of mathematics and physics. The applicant and his collaborators have studied the theory of Hardy spaces on various underlying spaces, including variable Hardy spaces, (Musielak-)Orlicz-Hardy spaces and their variants associated with operators. Based on these, in this project, via combining the theory of Hardy spaces and the theory of Amalgam spaces, which is widely used in time-frequency analysis, the applicant and collaborators will develop Hardy spaces related to (weighted) Amalgam spaces and established a complete real-variable theory of them, including the atomic and molecular decomposition, characterizations via Riesz transforms and Littlewood-Paley functions, duality and interpolation et al. Moreover, the project will further develop more general Amalgam type Besov-Triebel-Lizorkin spaces and consider the relations among these spaces and the classical modulation spaces, Besov spaces and Triebel-Lizorkin spaces, as well as their applications in the related study of boundedness of operators.