  We demonstrate generation of 7.6 fs near-UV pulses centered at 400 nm via
8-fold soliton-effect self-compression in an Ar-filled hollow-core
kagom\'e-style photonic crystal fiber with ultrathin core walls. Analytical
calculations of the effective compression length and soliton order permit
adjustment of the experimental parameters, and numerical modelling of the
nonlinear pulse dynamics in the fiber accurately predict the spectro-temporal
profiles of the self-compressed pulses. After compensation of phase distortion
introduced by the optical elements along the beam path from the fiber to the
diagnostics, 71% of the pulse energy was in the main temporal lobe, with peak
powers in excess of 0.2 GW. The convenient set-up opens up new opportunities
for time-resolved studies in spectroscopy, chemistry and materials science.
