非齐度量测度空间上的Herz型Hardy空间

Herz type Hardy spaces on non-homogeneous metric measure space

设(X, d,μ)是一个同时满足上双倍条件和几何双倍条件的非齐度量测度空间.本文首先引进了非齐度量测度空间上的Herz空间,并利用中心块得到了该空间的分解定理.然后,根据离散系数K_(B,S)^((ρ),p),引入了非齐度量测度空间上的原子Herz型Hardy空间与分子Herz型Hardy空间,并证明了原子Herz型Hardy空间和分子Herz型Hardy空间的等价性.最后作为应用,本文讨论了Calderón-Zygmund算子在这些空间上的有界性.

Let（X, d, μ） be a non-homogeneous metric measure space satisfying both the geometrically doubling and the upper doubling conditions. In this paper, the Herz spaces on the non-homogeneous metric measure space are introduced. Then the decomposition of the Herz space by the central blocks is obtained. The atomic Herz type Hardy spaces and the molecular Herz type Hardy spaces on the non-homogeneous metric measure space via the discrete coefficient K（B,S）-（（ρ）,p）,are also defined. In addition, the equivalence of the atomic Herz type Hardy spaces and the molecular Herz type Hardy spaces is established. As the applications of these spaces, some boundedness of Calderón-Zygmund operators on the Herz type Hardy spaces are discussed.