Geodesic
Atomic decomposition of finite signed measures on compacts of R^n
Francesca Angrisani1 ; Giacomo Ascione1 ; Gianluigi Manzo1
1 Universitá degli Studi di Napoli Federico II, Dipartimento di Matematica e Applicazioni
Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 643-654.

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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 $\mathbf{R}^n$ 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 $M(K)$ 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.
Keywords: Lipschitz space, atomic decomposition, duality, Kantorovich-Rubinstein norm

Francesca Angrisani 1 ; Giacomo Ascione 1 ; Gianluigi Manzo 1

1 Universitá degli Studi di Napoli Federico II, Dipartimento di Matematica e Applicazioni 
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Francesca Angrisani; Giacomo Ascione; Gianluigi Manzo. Atomic decomposition of finite signed measures on compacts of R^n. Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 643-654. http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a3/