  A theory of transport through semiconductor nanostructures in the fractional
quantum Hall regime is proposed, based on a model of composite fermion edge
states. Adiabatic and non-adiabatic constrictions and constrictions containing
artificial impurities are studied as examples. The results obtained, including
the temperature dependent behavior of Aharonov-Bohm resonances in the
fractional regime, are in good agreement with experiments. The temperature
dependence predicted by the composite fermion theory for features in the
two-terminal conductance of both adiabatic constrictions and constrictions with
artificial impurities, is close to that expected from ordinary Fermi liquid
phenomenology. However there are significant differences that should be
detectable by careful measurements. Some differences between the present
results and those obtained from Luttinger liquid models are discussed in the
context of the available experimental data.
