Two Remarks on Primary Spaces

Abstract

We prove that for any operator $T$ on $ \ell^\infty(H^1 (\bT))$, the identity factores through $T$ or $\Id - T$. We re-prove analogous results of H.M. Wark for the spaces $\ell^infty(H^p(\bT))$, $1<p<\infty$. In the present paper direct combinatorics of colored dyadic intervals replaces the dependence on Szemeredi's theorem in the work of H. M. Wark.