Duality and distance formulas in Lipschitz–Hölder spaces

  • Francesca Angrisani

    Università degli Studi di Napoli Federico II, Italy
  • Giacomo Ascione

    Università degli Studi di Napoli Federico II, Italy
  • Luigi D'Onofrio

    Università degli Studi di Napoli Parthenope, Italy
  • Gianluigi Manzo

    Università degli Studi di Napoli Federico II, Italy
Duality and distance formulas in Lipschitz–Hölder spaces cover
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Abstract

For a compact metric space (K,ρ)(K,\rho), the predual of Lip(K,ρ)Lip(K,\rho) can be identified with the normed space M(K)M(K) of finite (signed) Borel measures on KK equipped with the Kantorovich–Rubinstein norm, this is due to Kantorovich [20]. Here we deduce atomic decomposition of M(K)\mathcal M(K) by mean of some results from [10]. It is also known, under suitable assumption, that there is a natural isometric isomorphism between Lip(K,ρ)Lip(K,\rho) and (lip(K,ρ))(lip(K, \rho))^{**} [15]. In this work we also show that the pair (lip(K,ρ),Lip(K,ρ))(lip(K,\rho),Lip(K,\rho)) can be framed in the theory of oOo–O type structures introduced by K. M. Perfekt.

Cite this article

Francesca Angrisani, Giacomo Ascione, Luigi D'Onofrio, Gianluigi Manzo, Duality and distance formulas in Lipschitz–Hölder spaces. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), no. 2, pp. 401–419

DOI 10.4171/RLM/897