2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125314The 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 $\|f\|_{\hat{H^{s,p}}} := \| < ξ>^s \hat{f}\|_{L^{p'}}$, 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.15 pagesAnalysis of PDEs35Q40; 35L70text