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The conjugation operator on $A\sb q(G)$

1994
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Proceedings of the American Mathematical Society
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Let G be a compact abelian group and r its dual. For 1 < q < oo , the space Aq(G) is defined as Aq(G) = {f\feLx(G), felq(T)} with the norm \\f\\Aq = ll/ll¿i + \\f\\tq ■ We prove: Let G be a compact, connected abelian group and P any fixed order on T. If q > 2 and is a Young's function, then the conjugation operator H does not extend to a bounded operator from Aq(G) to the Orlicz space L't'(G). Let G be a compact abelian group and Y its dual. For 1 < q < oo, the space Aq(G) is defined as with

doi:10.1090/s0002-9939-1994-1181167-4
fatcat:ytthf2cohjcrhbe5bxlqnthaeu