THE CONJUGATION OPERATOR ON A(Q)(G)

Let G be a compact abelian group and GAMMA its dual. For 1 less-than-o r-equal-to q < infinity, the space A(q)(G) is defined as A(q)(G) = {f\ f is-an-element-of L1(G), f is-an-element-of l(q)(GAMMA)} with the nor m \\f\\Aq = \\f\\L1 + \\f\\lq. We prove: Let G be a compact, connected abelian group and P any fixed order on GAMMA. If q > 2 and phi is a Y oung's function, then the conjugation operator H does not extend to a bounded operator from A(q)(G) to the Orlicz space L(phi)(G).