  We obtain weighted $L^2$ Strichartz estimates for Schr\"odinger equations
$i\partial_tu+(-\Delta)^{a/2}u=F(x,t)$, $u(x,0)=f(x)$, of general orders $a>1$
with radial data $f,F$ with respect to the spatial variable $x$, whenever the
weight is in a Morrey-Campanato type class. This is done by making use of a
useful property of maximal functions of the weights together with
frequency-localized estimates which follow from using bilinear interpolation
and some estimates of Bessel functions. As consequences, we give an affirmative
answer to a question posed in \cite{BBCRV} concerning weighted homogeneous
Strichartz estimates, and improve previously known Morawetz estimates. We also
apply the weighted $L^2$ estimates to the well-posedness theory for the
Schr\"odinger equations with time-dependent potentials in the class.
