G is a compact abelian group. The main result of this paper is that if T is a (p,1) multiplier, 1 < p ≦ 2, then T is a (p,s) multiplier for all s in the range 1 ≦ s < p and also an (∕γ,γ) multiplier for p < r < p′( p′ conjugate of p).
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