  In this paper, we consider the cubic nonlinear Schrodinger equation, and the
Hartree equation, with sufficiently regular convolution potential, both on the
real line. We are interested in bounding the growth of high Sobolev norms of
solutions to these equations. Since the cubic NLS is completely integrable, it
makes sense to bound only the fractional Sobolev norms of solutions, whose
initial data is of restricted smoothness. For the Hartree equation, we consider
all Sobolev norms. For both equations, we derive our results by using an
appropriate frequency decomposition. In the case of the cubic NLS, this method
allows us to recover uniform bounds on the integral Sobolev norms, up to a
factor of $t^{0+}$. For the Hartree equation, we use the same method as in our
previous work on $S^1$, and the improved Strichartz estimate to obtain a better
bound than we previously obtained in the periodic setting.
