Local well-posedness of the two-dimensional Dirac-Klein-Gordon equations in Fourier-Lebesgue spaces

The local well-posedness problem is considered for the Dirac-Klein-Gordon system in two space dimensions for data in Fourier-Lebesgue spaces ${\widehat{H}}^{s,r}$ , 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.