基于混合范数函数空间上的算子及交换子性质研究

本项目基于已有的混合范数空间结论和方法，受启发于泛函分析、几何分析和概率论中的一些思想, 结合调和分析的经典方法理论, 本项目将研究（变指数）混合范数的Herz空间、Morrey型空间、混合Herz-Hardy空间等的性质，以及得到一些经典算子在混合范函数空间上的有界估计；研究基于混合范数Lebesgue空间的Muckenhoupt权理论、多线性理论；本研究将深化现有函数空间理论和算子理论，也将进一步推动调和分析理论的发展。

Based on the known results and tools from some papers related to mixed-norm function spaces, motivated by some idea from functional analysis, geometric analysis and probability and associated with some classical methods and theories in harmonic analysis, this project is to study the properties of (variable) mixed-norm Herz spaces, (variable) Morrey-type spaces, (variable) mixed-norm Herz-Hardy spaces and get the boundedness of some classical operators. In addition, the second aim of our project leads to study the Muckenhoupt weight theory and the multilinear operator theory based on mixed-norm Lebesgue spaces. All results obtained in this project will deepen the known theories of mixed-norm function spaces and operators and improve harmonic analysis in some sense.