On the strongly subdifferentiable points in Lipschitz-free spaces

Abstract

[EN] In this paper, we present some sufficient conditions on a metric space M for which every molecule is a strongly subdifferentiable (SSD, for short) point in the Lipschitz- free space F(M) over M. Our main result reads as follows: if (M , d) is a metric space and gamma > 0, then there exists a (not necessarily equivalent) metric d(gamma) in M such that every finitely supported element in F(M, d(gamma)) is an SSD point. As an application of the main result, it follows that if M is uniformly discrete and epsilon > 0 is given, there exists a metric space N and a (1 + e)-bi-Lipschitz map Phi : M -> N such that the set of all SSD points in F(N) is dense.