本项目拟研究的是非交换Orlicz-Lorentz-Hardy空间及其在非交换调和分析中的应用方面的问题。该课题是非交换空间理论与调和分析交叉研究的一个课题。首先我们将应用相对完善的非交换Lp空间和非交换Orlicz空间的研究方法来研究次对角代数的非交换Orlicz-Lorentz空间分解性质，非交换Orlicz-Lorentz空间的对偶空间，广义对偶空间，插值空间等问题。由此并应用经典的非交换Hardy空间和非交换对称空间的研究方法来研究非交换Orlicz-Lorentz-Hardy空间中的一系列问题，包括Szego型和Riesz型分解定理，外算子的性质，A-不变子空间，插值空间，对偶空间，Hartman-Wintner定理，Adamyan-Arov-Krein定理等问题。我们将首先在有限von Neumann代数的情形下考虑以上问题，然后在半有限情形下继续推进以上问题的研究。

In the project, some problems on noncommutative Orlicz-Lorentz-Hardy spaces and its applications in noncommutative Harmonic Analysis are considered. The project is a crossing one of the theory of noncommutative spaces and Harmonic Analysis. In the first, the noncommutative Orlicz-Lorentz factorization property of subdiagonal algebras, as well as dual spaces, generalized dual spaces and interpolation spaces etc. are established, by an application of the relatively excellent theoretical method in the research on noncommutative Lp spaces and noncommutative Orlicz spaces. Based on this part of research, we make every effort to adopt the remarkable techniques, which were developed in the research on noncommutative Hardy spaces and noncommutative symmetric spaces, to study a series of problems in noncommutative Orlicz-Lorentz-Hardy spaces, including Szego type and Riesz type factorization theorem, A-invariant subspaces, interpolation spaces, dual spaces, Hartman-Wintner spectral inclusion theorem and Adamyan-Arov-Krein theorem etc. All the above problems will be firstly considered in the case of finite von Neumann algebra, thus we will extend the research to the case of semi-finite.