On Lipschitz-Lorentz Spaces and Their Zygmund Classes

Abstract

Let G be a metrizable locally compact abelian group. We prove that (L1(G), lip (α, pq)), lip (α, pq), (L1(G), Lip (α, pq)) and Lip(α, pq) are isometrically isomorphic, where Lip(α, pq) and lip (α, pq) denote the Lipschitz-Lorentz spaces defined on G, (L1(G), A) is the space of multipliers from L1(G) to A and lip (α, pq) denotes the relative completion of lip (α, pq). Also, we characterize the space of multipliers from Lorentz spaces to the Lipschitz-Lorentz-Zygmund classes LΛ*(α, pq; G) and Lλ*(α, pq; G).