  In this paper, we characterize parabolic Besov and parabolic Sobolev spaces
in ${\bf R}^{n+1}$ and ${\bf R}^{n+1}_T, \,\, T > 0$. We also, study the
relation between parabolic Besov spaces in ${\bf R}^{n}_T, \,\, T > 0$ and
standard Besov space in $\R$.
