This paper treats near-rings of zero-preserving Lipschitz functions on metric spaces that are also abelian groups, using pointwise addition of functions as addition and composition of functions as multiplication. We identify a condition on the metric ensuring that the set of all such Lipschitz functions is a near-ring, and we investigate the complications that arise from the lack of left distri...

We show that the Lipschitz structure of a separable quasi-Banach space does not determine, in general, its linear structure. Using the notion of the Arens-Eells p-space over a metric space for 0 < p ≤ 1 we construct examples of separable quasi-Banach spaces which are Lipschitz isomorphic but not linearly isomorphic.

In this paper we extend classical Titchmarsh theorems on the Fourier–Helgason transform of Lipschitz functions to setting L p -space Damek–Ricci spaces. As consequences, quantitative Riemann–Lebesgue estimates are obtained and an integrability result for is developed extending ideas used by in one dimensional setting.