Atomic decomposition of finite signed measures on compacts of R^n

Authors

  • Francesca Angrisani Universitá degli Studi di Napoli Federico II, Dipartimento di Matematica e Applicazioni
  • Giacomo Ascione Universitá degli Studi di Napoli Federico II, Dipartimento di Matematica e Applicazioni
  • Gianluigi Manzo Universitá degli Studi di Napoli Federico II, Dipartimento di Matematica e Applicazioni

Keywords:

Lipschitz space, atomic decomposition, duality, Kantorovich-Rubinstein norm

Abstract

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.
Section
Articles

Published

2021-08-02

How to Cite

Angrisani, F., Ascione, G., & Manzo, G. (2021). Atomic decomposition of finite signed measures on compacts of R^n. Annales Fennici Mathematici, 46(2), 643–654. Retrieved from https://afm.journal.fi/article/view/110566