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The conjugation operator on \(A_{q}(G)\). (English) Zbl 1042.43001

The main result of the paper is: Let \(G\) be a compact, connected abelian group and \(P\) a fixed order on the dual of \(G\). If \(q > 2\), then the conjugation operator \(H\) does not extend to a bounded operator on \(A-q (G)\).

MSC:

43A17 Analysis on ordered groups, \(H^p\)-theory
42A50 Conjugate functions, conjugate series, singular integrals
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