  We prove that the Cauchy problem for the Dirac-Klein-Gordon equations in two
space dimensions is locally well-posed in a range of Sobolev spaces of negative
index for the Dirac spinor, and an associated range of spaces of positive index
for the meson field. In particular, we can go below the charge norm, that is,
the $L^2$ norm of the spinor. We hope that this can have implications for the
global existence problem, since the charge is conserved. Our result relies on
the null structure of the system, and bilinear space-time estimates for the
homogeneous wave equation.
