We prove that the Lipschitz-free space over a Banach space X of density κ, denoted by F (X), is linearly isomorphic to the l 1 -sum of κ copies of F (X) . This provides an extension of a previous result from Kaufmann in ...

We consider a class of retarded functional differential equations with preas-signed moments of impulsive effect and we study the Lipschitz stability of solutions of these equations using the theory of generalized ordinary ...

We provide some necessary and sufficient conditions for a proper lower semicontinuous convex function, defined on a real Banach space, to be locally or globally Lipschitz continuous. Our criteria rely on the existence of ...

We develop tools for proving isomorphisms of normed spaces of Lipschitz functions over various doubling metric spaces and Banach spaces. In particular, we show that Lip0(Zd) ≃ Lip0(Rd), for all d ∈ N. More generally, ...

Este trabalho é dividido em duas partes. Na primeira parte, apresentamos uma introdução aos espaços de funções de Lipschitz e aos espaços Lipschitz livres, tendo como ênfase a geometria desses espaços. Na segunda parte, ...

The convex cone SC1 SLip(X) of real-valued smooth semi-Lipschitz functions on a Finsler manifold X is an order-algebraic structure that captures both the differentiable and the quasi-metric feature of X. In this work ...

Epi-Lipschitz sets in normed spaces are represented as sublevel sets of Lipschitz functions satisfying a so-called qualification condition. Canonical representations through the signed distance functions associated with ...

We investigate the problem of classifying the Banach spaces Lip0(C(K)) for Hausdorff compacta K. In particular, sufficient conditions are established for a space Lip0(C(K)) to be isomorphic to Lip0(c0(Γ )) for some ...

We establish a relation between Lipschitz operator ideals and linear operator ideals, which fits in the framework of Galois connection between lattices. We use this relationship to give a criterion which allows us to ...

We study Lipschitz-free spaces over compact and uniformly discrete metric spaces enjoying certain high regularity properties - having group structure with left-invariant metric. Using methods of harmonic analysis we show ...