  In this work we establish a weighted $L^2-L^2$ estimate for inhomogeneous
wave equation in 3-D, by introducing a Morawetz multiplier with weight of power
$s(1<s<2)$, and then integrating on the light cones and $t$ slice. With this
weighted $L^2-L^2$ estimate in hand, we may give a new proof of global
existence for small data Cauchy problem of semilinear wave equation with
supercritical power in 3-D. What is more, by combining the Huygens' principle
for wave equations in 3-D, the global existence for semilinear wave equation
with scale invariant damping in 3-D is established.
