Hankel operators on Lp(ℝ+) and their p-completely bounded multipliers

We show that for any 1 < p < ∞, the space Hank p ‫ޒ(‬ + ) ⊆ B(L p ‫ޒ(‬ + )) of all Hankel operators on L p ‫ޒ(‬ + ) is equal to the w * -closure of the linear span of the operators θ u :We deduce that Hank p ‫ޒ(‬ + ) is the dual space of A p ‫ޒ(‬ + ), a half-line analogue of the Figà-Talamanca-Herz algebra A p ‫.)ޒ(‬ Then we show that a function m : ‫ޒ‬ * + → ‫ރ‬ is the symbol of a p-completely bounded multiplier Hank p ‫ޒ(‬ + ) → Hank p ‫ޒ(‬ + ) if and only if there exist α ∈ L ∞ ‫ޒ(‬ + ; L p ( )) and β ∈ L ∞ ‫ޒ(‬ + ; L p ′ ( )) such that m(s + t) = ⟨α(s), β(t)⟩ for a.e.(s, t) ∈ ‫ޒ‬ * 2 + .We also give analogues of these results in the (easier) discrete case.