  In [19-20], we have established the existence and singularity structures of
low regularity solutions to the semilinear generalized Tricomi equations in the
degenerate hyperbolic regions and to the higher order degenerate hyperbolic
equations, respectively. In the present paper, we shall be concerned with the
low regularity solution problem for the semilinear mixed type equation
$\p_t^2u-t^{2l-1}\Delta u= f(t,x,u)$ with an initial data $u(0,x)=\varphi(x)\in
H^{s}(\Bbb R^n)$ ($0\le s<\f{n}{2}$), where $(t,x)\in\Bbb R \times\Bbb R^n$,
$n\ge 2$, $l\in\Bbb N$, $f(t,x,u)$ is $C^1$ smooth in its arguments and has
compact support with respect to the variable $x$. Under the assumption of the
subcritical growth of $f(t,x,u)$ on $u$, we will show the existence and
regularity of the considered solution in the mixed type domain $[-T_0, T_0]
\times \R^n $ for some fixed constant $T_0>0$.
