THE CONJUGATION OPERATOR ON Aq(G)
نویسنده
چکیده
with the norm ‖f‖Aq = ‖f‖L1 +‖f̂‖lq . Then Aq(G) is a commutative semisimple Banach algebra with maximal ideal space Γ , in which the set of trigonometric polynomials is dense [4]. The Ap-spaces have been studied in [1, 6]. If G is, in addition, a connected group, then its dual can be ordered; there exists a semigroup P ⊂ Γ such that P∩−P = {0}, P∪−P = Γ (see [5]), and we say that γ ∈ Γ is positive if γ ∈ P . If f =γ∈F f̂ (γ)γ is a trigonometric polynomial, the conjugation operator H is defined as
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