  The complete set of ${\cal O}(\alpha)$ QED corrections with soft photon
exponentiation to the process $ep \rightarrow eX$ in mixed variables
($y=y_h,Q^2=Q_l^2$) is calculated in the quark parton model, including the
lepton-quark interference and the quarkonic corrections which were unknown so
far. The interference corrections amount to few percent or less and become
negligible at small $x$. The leading logarithmic terms proportional to
$\ln(Q^2/m_q^2)$ from radiation off quarks are discussed and the
non-logarithmic quarkonic corrections found to be negligible for almost all
experimentally accessible $x$ and $y$.
