... gσ,φ1σ ∈ K for each σ ∈ R. Now from the uniformcontinuity of Fbon bounded subsets of X, it obviously follows that Fbis uniformly continuouson K uniformly for each t ∈ R. Therefore for every ... PAP0Lp0, 1, X. First of all, note that the uniformlycontinuity of F on bounded subsets K ⊂ X yields the uniform continuity of its Bohr transformFbon bounded subsets of X. Since both g,φ1are ... 11Concrete examples of Xαinclude D−Aα for α ∈ 0, 1, the domains of the f ractionalpowers of A, the real interpolation spaces DAα, ∞, α ∈ 0, 1, defined as the space of allx ∈ X suchxα...