  Let $u=u(t,{\bf x},{\bf p})$ satisfy the transport equation $\frac {\partial
u}{\partial t}+\frac {{\bf p}}{p_0}\frac{\partial u}{\partial{\bf x}}=f$, where
$f=f(t,\bf x,\bf p)$ belongs to $ L^{p}((0,T)\times {\bf R}^{3}\times {\bf
R}^{3})$ for $1<p<\infty$ and $\frac {\partial}{\partial t}+\frac {{\bf
p}}{p_0}\frac{\partial}{\partial{\bf x}}$ is the relativistic-free transport
operator. We show the regularity of $\int_{{\bf R}^{3}}u(t, {\bf x}, {\bf
p})d{\bf p}$ using the same method as given by Golse, Lions, Perthame and
Sentis. This average regularity is considered in terms of fractional Sobolev
spaces and it is very useful for the study of the existence of the solution to
the Cauchy problem on the relativistic Boltzmann equation.
