  We study norm inequalities for the Fourier transform, namely,
\begin{equation}\label{introduction} \|\widehat f\|_{X_{p,q}^\lambda} \lesssim
\|f\|_{Y}, \end{equation} where $X$ is either a Morrey or Campanato space and
$Y$ is an appropriate function space. In the case of the Morrey space we
sharpen the estimate $ \|\widehat f\|_{M_{p,q}^\lambda} \lesssim
\|f\|_{L_{s',q}},$ $ s\geq 2,$ $\frac{1}{s} = \frac{1}{p}-\frac{\lambda}{n}.$
We also show that \eqref{introduction} does not hold when both $X$ and $Y$ are
Morrey spaces.
  If $X$ is a Campanato space, we prove that \eqref{introduction} holds for $Y$
being the truncated Lebesgue space.
