  We calculate the two-point massless QCD correlator of nonlocal (composite)
vector quark currents with chains of fermion one-loop radiative corrections
inserted into gluon lines. The correlator depends on the Bjorken fraction $x$
related to the composite current and, under large-$\beta_0$ approximation,
gives the main contributions in each order of perturbation theory. In the
mentioned approximation, these contributions dominate the endpoint behavior of
the leading-twist distribution amplitudes of light mesons in the framework of
QCD sum rules. Based on this, we analyze the endpoint behavior of these
distribution amplitudes for $\pi$ and longitudinally polarized $\rho^\|$ mesons
and find inequalities for their moments.
