  We study the transverse-momentum distribution of hadrons produced in
semi-inclusive deep-inelastic scattering (SIDIS). We consider cross sections
for various combinations of polarizations of the initial lepton and nucleon or
the produced hadron, for which we perform the resummation of large
double-logarithmic perturbative corrections arising at small transverse
momentum. We present phenomenological results for the processes $lp\to l\pi X$
with longitudinally polarized leptons and protons. We discuss the impact of the
perturbative resummation and of estimated non-perturbative contributions on the
corresponding cross sections and their spin asymmetry. Our results should be
relevant for ongoing studies in the COMPASS experiment at CERN, and for future
experiments at the proposed eRHIC collider at BNL.
