We prove that for an operator T on ℓ∞(H1 ()), respectively ℓ∞(L1 ()), the identity factors through T or Id - T. Hence ℓ∞(H1 ()) and ℓ∞(L1 ()) are primary spaces. We re-prove analogous results of H.M. Wark for the spaces ℓ∞(Hp()), 1 < p < ∞. In the present paper direct combinatorics of colored dyadic intervals replaces the dependence on Szemerédi's theorem in [11].