Duality and Distance Formulas in Lipschitz-Hölder Spaces

For a compact metric space K; rÞ, the predual of LipK; rÞ can be identified with the normed space MKÞ of finite (signed) Borel measures on K equipped with the Kantorovich-Rubinstein norm, this is due to Kantorovich [20]. Here we deduce atomic decomposition of MKÞ by mean of some results from [10]. It is also known, under suitable assumption, that there is a natural isometric isomorphism between LipK; rÞ and lipK; rÞÞ__[15]. In this work we also show that the pair lipK; rÞ; LipK; rÞÞ can be framed in the theory of o-O type structures introduced by K. M. Perfekt.