  We prove hp-optimal error estimates for the original DG method when
approximating solutions to first-order hyperbolic problems with constant
convection fields in the L2 and DG norms. The main theoretical tools used in
the analysis are novel hp-optimal approximation properties of the special
projector introduced in [Cockburn, Dong, Guzman, SINUM, 2008]. We assess the
theoretical findings on some test cases.
