  The 1D Cauchy problem for the Dirac-Klein-Gordon system is shown to be
locally well-posed for low regularity Dirac data in $\hat{H^{s,p}}$ and wave
data in $\hat{H^{r,p}} \times \hat{H^{r-1,p}}$ for $1<p\le 2$ under certain
assumptions on the parameters r and s, where $\|f\|_{\hat{H^{s,p}}} := \| < \xi
>^s \hat{f}\|_{L^{p'}}$, generalizing the results for $p=2$ by Selberg and
Tesfahun. Especially we are able to improve the results from the scaling point
of view with respect to the Dirac part.
