We characterize the range of some spaces of functions by the Fourier transform associated with the spherical mean operator R and we give a new description of the Schwartz spaces. Next, we prove a Paley-Wiener and a Paley-Wiener-Schawrtz theorems.
We extend to the case 1 < p the results obtained by Geymonat and Krasucki for p = 2 on the characterization of the traces of W2,p(Ω) for a bounded Lipschitz domain.
Let G be a locally compact group. We use the canonical operator space structure on the spaces for p ∈ [1,∞] introduced by G. Pisier to define operator space analogues of the classical Figà-Talamanca-Herz algebras . If p ∈ (1,∞) is arbitrary, then and the inclusion is a contraction; if p = 2, then OA₂(G) ≅ A(G) as Banach spaces, but not necessarily as operator spaces. We show that is a completely contractive Banach algebra for each p ∈ (1,∞), and that completely contractively for amenable...