We prove that all extreme points of the unit ball a Lipschitz-free space over compact metric have finite support. Combined with previous results, this completely characterizes and implies them are also in bidual ball. For proof, we develop some properties an integral representation functionals on Lipschitz spaces originally due to K. de Leeuw.

The characterization by weighted Lipschitz continuity is given for the Bloch space on the unit ball of Rn. Similar results are obtained for little Bloch and Besov spaces.

In this paper, we establish the boundedness of commutators generated by weighted Lipschitz functions and Calderón-Zygmund singular integral operators on weighted Herz spaces.

In this paper, using Lipschitz continuity of general (H, η)-monotone operators, a type of implicit variational-like inclusion problems in uniformly smooth Banach spaces are solved.

This paper gives a characterization of a class of surjective isometries on spaces of Lipschitz functions with values in a finite dimensional complex Hilbert space.

We show that the Scott topology induces a topology for real-valued Lipschitz maps on Banach spaces which we call the L-topology. It is the weakest topology with respect to which the L-derivative operator, as a second order functional which maps the space of Lipschitz functions into the function space of non-empty weak* compact and convex valued maps equipped with the Scott topology, is continuo...

We show that if Y is a separable subspace of a Banach space X such that both X and the quotient X/Y have Cp-smooth Lipschitz bump functions, and U is a bounded open subset of X, then, for every uniformly continuous function f : Y ∩U → R and every ε > 0, there exists a Cp-smooth Lipschitz function F : X → R such that |F (y)− f(y)| ≤ ε for every y ∈ Y ∩U . If we are given a separable subspace Y o...

We answer a question of Aharoni by showing that every separable metric space can be Lipschitz 2-embedded into c0 and this result is sharp; this improves earlier estimates of Aharoni, Assouad and Pelant. We use our methods to examine the best constant for Lipschitz embeddings of the classical `p-spaces into c0 and give other applications. We prove that if a Banach space embeds almost isometrical...