In this talk, I will present a joint work with W. Yang and C. Yuan on the weak decomposition of the Hardy and boundedness of the small Hankel operator on the Hardy space. It is well known that a function $f\in H^p(D)$, the Hardy space over the unit disc $D$ can be written as the product of functions $f_1$ and $ f_2 $ in $H^{2p}(D)$ with $\|f\|_{H^p}=\|f_1|_{2p} \|f_2\|_{H^2}$. This is no longer true for the Hardy space on the unit ball $B_n$ in ${\bf C}^n$ when $n>1$. A well known theorem was proved by Coiffman, Rochberg and Weiss (Ann. of Math., 1976) that there is a weak decomposition for $H^1(B^n)$ through atomic decomposition. Their theorem has been proved true for $H^p$ when $p\le 1$. In this talk,I will show that it remains true when $p>1$. As a consequence, we obtained boundedness of the small Hankel operator on Hardy spaces.