  The local well-posedness problem is considered for the Dirac-Klein-Gordon
system in two space dimensions for data in Fourier-Lebesgue spaces
$\hat{H}^{s,r}$ , where $\|f\|_{\hat{H}^{s,r}} = \| \langle \xi \rangle^s
\hat{f}\|_{L^{r'}}$ and $r$ and $r'$ denote dual exponents. We lower the
regularity assumptions on the data with respect to scaling improving the
results of d'Ancona, Foschi and Selberg in the classical case $r=2$ . Crucial
is the fact that the nonlinearities fulfill a null condition as detected by
these authors.
