  The solution of the Dirac - Klein - Gordon system in two space dimensions
with Dirac data in H^s and wave data in H^{s+1/2} x H^{s-1/2} is uniquely
determined in the natural solution space C^0([0,T],H^s) x
C^0([0,T],H^{s+\frac1/2}), provided s > 1/30 . This improves the uniqueness
part of the global well-posedness result by A. Gruenrock and the author, where
uniqueness was proven in (smaller) spaces of Bourgain type. Local
well-posedness is also proven for Dirac data in L^2 and wave data in H^{3/5}+}
x H^{-2/5+} in the solution space C^0([0,T],L^2) x C^0([0,T],H^{3/5+}) and also
for more regular data.
