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.
