On the compactness theorem for differential forms

Kichenassamy found conditions under which the space $W_p^k$ of differential forms on a closed manifold $M$ with the norm $\|\omega\|W_p=\|\omega\|L_p+\|d\omega\|L_p$ embeds compactly in the space $F_p^k$ of currents on $M$ with the norm $\inf\limits_{\varphi\in L_q}\{\|\omega-d\varphi\|L_q+\|\varphi\|L_q\}$. We give a version of Kichenassamy's theorem for an arbitrary Banach complex and, in particular, for an elliptic differential complex on a closed manifold.