The algebra of functions with Fourier transforms in a given function space
1973 ◽
Vol 9
(1)
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pp. 73-82
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Keyword(s):
Let G be a locally compact abelian group and Ĝ be its dual group. For 1 ≤ p < ∞, let Ap (G) denote the set of all those functions in L1(G) whose Fourier transforms belong to Lp (Ĝ). Let M(Ap (G)) denote the set of all functions φ belonging to L∞(Ĝ) such that is Fourier transform of an L1-function on G whenever f belongs to Ap (G). For 1 ≤ p < q < ∞, we prove that Ap (G) Aq(G) provided G is nondiscrete. As an application of this result we prove that if G is an infinite compact abelian group and 1 ≤ p ≤ 4 then lp (Ĝ) M(Ap(G)), and if p > 4 then there exists ψ є lp (Ĝ) such that ψ does not belong to M(Ap (G)).
1978 ◽
Vol 18
(1)
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pp. 1-11
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1984 ◽
pp. 261-269
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1987 ◽
Vol 39
(1)
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pp. 123-148
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Keyword(s):
1972 ◽
Vol 71
(1)
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pp. 63-66
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1997 ◽
Vol 146
(1)
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pp. 62-115
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2013 ◽
Vol 160
(5)
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pp. 682-684
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Keyword(s):
1994 ◽
Vol 17
(3)
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pp. 475-478
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1993 ◽
Vol 54
(1)
◽
pp. 97-110
1983 ◽
Vol 35
(1)
◽
pp. 123-131
Keyword(s):
1971 ◽
Vol 70
(1)
◽
pp. 31-47
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Keyword(s):