We extend the Hardy-Littlewood duality theorem to any locally compact abelian group G, namely, if {L^q}(G)(2 < q < ∞ ) has the upper majorant property, then {L^q}(G) has the lower majorant property, {p
- 1} + {q
- 1} = 1. This settles the question of exactly which {L^p}(G) has the lower majorant property.
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