  A class of subharmonic functions are proved to have the growth estimates
  $u(x)=
o(x_n^{1-\frac{\alpha}{p}}|x|^{\frac{\gamma}{p}+\frac{n-1}{q}-n+\frac{\alpha}{p}})$
at infinity in the upper half space of ${\bf R}^{n}$, which generalizes the
growth properties of analytic functions and harmonic functions.
