论文标题
有限签名的原子分解$ \ mathbb {r}^n $
Atomic decomposition of finite signed measures on compacts of $\mathbb{R}^n$
论文作者
论文摘要
最近，$ o-o $关系中的Banach Space $（e_0，e）$以及$ e_0^{**} = e $的对成对引起了兴趣。众所周知，这可以针对合适的度量空间上的Lipschitz空间进行。在本文中，我们考虑了与Euclidean公制的紧凑型子集$ k $的$ \ MATHBB {r}^n $，该公制没有给出$ o-o-o $结构，但是我们使用了有关这些对这些理论的一部分，以找到这些对原子的原子分解，以$ lip（k）$。特别是，由于有限$ \ mathfrak {m}（k）$在$ k $上签署的措施，当与Kantorovich-Rubinstein Norm赋予时，具有双空间$ LIP（K）$，我们可以为此空间提供原子分解。
Recently there has been interest in pairs of Banach spaces $(E_0,E)$ in an $o-O$ relation and with $E_0^{**}=E$. It is known that this can be done for Lipschitz spaces on suitable metric spaces. In this paper we consider the case of a compact subset $K$ of $\mathbb{R}^n$ with the euclidean metric, which does not give an $o-O$ structure, but we use part of the theory concerning these pairs to find an atomic decomposition of the predual of $Lip(K)$. In particular, since the space $\mathfrak{M}(K)$ of finite signed measures on $K$, when endowed with the Kantorovich-Rubinstein norm, has as dual space $Lip(K)$, we can give an atomic decomposition for this space.
