  The Cauchy problem for the classical Dirac-Klein-Gordon system in two space
dimensions is globally well-posed for L^2 Schoedinger data and wave data in
H^{1/2} \times H^{-1/2}. In the case of smooth data there exists a global
smooth (classical) solution. The proof uses function spaces of Bourgain type
based on Besov spaces - previously applied by Colliander, Kenig and Staffilani
for generalized Benjamin-Ono equations and also by Bejenaru, Herr, Holmer and
Tataru for the 2D Zakharov system - and the null structure of the system
detected by d'Ancona, Foschi and Selberg, and a refined bilinear Strichartz
estimate due to Selberg. The global existence proof uses an idea of Colliander,
Holmer and Tzirakis for the 1D Zakharov system.
