Sharp null form estimates for the wave equation

Null form estimates (from $\dot{H}^{\alpha_1}\times\dot{H}^{\alpha_2}$ to $L^q_t(L^r_x)$) for the wave equation in ${\Bbb R}^{n+1}$ are studied. For $n\ge4,$ we obtain the sharp null form estimates except for the endpoints. For $n=2,\,3$ we obtain the estimates under the additional assumption $4/n<q$ when $2< r$.