Dirichlet型空间与Mobius不变空间一直是函数空间与算子理论领域很活跃的研究对象，其理论在位势理论、调和分析与偏微分方程领域有着深刻的应用。为了发展Dirichlet型空间理论并解决相关的Mobius不变空间中的一些问题，申请人、 N.G.Gogus和S.Pouliasis近期引入了一类Dirichlet型空间D_{μ,p}。本项目将研究D_{μ,p}空间与它生成的Mobius不变空间。研究内容包括D_{μ,p}空间的Hardy-Littlewood型定理、原子分解特征以及D_{μ,p}空间生成的Mobius不变空间的一般理论。我们也将利用D_{μ,p}空间与Bloch空间的关系来探索Bloch空间的Carleson测度这一个公开问题。通过本项目的研究，期望填补某些研究空白，寻求和发现新的研究途径和有效工具，建立较完备的D_{μ,p}空间及其生成的Mobius不变空间理论。

The study of Dirichlet type spaces and Mobius invariant spaces is very active in the field of function spaces and operator theory, which has been applied to potential theory, harmonic analysis and the partial differential equations. To develop the theory of Dirichlet type spaces and to consider some problems in some Mobius invariant spaces, the applicant, N.G.Gogus and S.Pouliasis introduced a class of Dirichlet type spaces denoted by D_{μ,p} recently. The aim of this project is to investigate D_{μ,p} spaces and Mobius invariant spaces generated by them, including the Hardy-Littlewood type theorem and the atomic decomposition theorem for D_{μ,p} spaces, the general theory of Mobius invariant spaces generated by D_{μ,p}. The project also considers the open problem of characterizing Carleson measures for the Bloch space via the theory of D_{μ,p} spaces. By seeking some new and valid methods, we hope to complete the theory of D_{μ,p} spaces and Mobius invariant spaces generated by them.