TAME Lp-MULTIPLIERS BY

0. Introduction. Let G be a compact abelian group and let Γ be its discrete dual group. Let 1 ≤ p, q ≤ ∞. A function m: Γ → C is called an (Lp, Lq) multiplier (or Lp multiplier if p = q) if for every f ∈ Lp(G) there is a function Tmf ∈ Lq(G) such that T̂mf(γ) = m(γ)f̂(γ