  A novel factorization formula is presented for the longitudinal structure
function $F_L$ near the elastic region $x \to 1$ of deeply inelastic
scattering. In moment space this formula can resum all contributions to $F_L$
that are of order $\ln^k N/N$. This is achieved by defining a new jet function
which probes the transverse momentum of the struck parton in the target at
leading twist. The anomalous dimension $\gamma_{J^\prime}$ of this new jet
operator generates in moment space the logarithmic enhancements coming from the
fragmentation of the current jet in the final state. It is also shown how the
suggested factorization for $F_L$ is related to the corresponding one for $F_2$
in the same kinematic region.
