Density and representation theorems for multipliers of type (p, q)
1967 ◽
Vol 7
(1)
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pp. 1-6
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Let G be a locally compact Abelian Hausdorff group (abbreviated LCA group); let X be its character group and dx, dx be the elements of the normalised Haar measures on G and X respectively. If 1 < p, q < ∞, and Lp(G) and Lq(G) are the usual Lebesgue spaces, of index p and q respectively, with respect to dx, a multiplier of type (p, q) is defined as a bounded linear operator T from Lp(G) to Lq(G) which commutes with translations, i.e. τxT = Tτx for all x ∈ G, where τxf(y) = f(x+y). The space of multipliers of type (p, q) will be denoted by Lqp. Already, much attention has been devoted to this important class of operators (see, for example, [3], [4], [7]).
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2013 ◽
Vol 95
(2)
◽
pp. 158-168
1991 ◽
Vol 14
(3)
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pp. 611-614
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1991 ◽
Vol 43
(2)
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pp. 241-250
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Keyword(s):
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