  We have developed a theory of the longitudinal $g$ factor of light holes in
semiconductor quantum wells. It is shown that the absolute value of the
light-hole $g$-factor can strongly exceed its value in the bulk and, moreover,
the dependence of the Zeeman splitting on magnetic field becomes non-linear in
relatively low fields. These effects are determined by the proximity of the
ground light-hole subband, $lh1$, to the first excited heavy-hole subband,
$hh2$, in GaAs/AlGaAs-type structures. The particular calculations are
performed in the framework of Luttinger Hamiltonian taking into account both
the magnetic field-induced mixing of $lh1$ and $hh2$ states and the mixing of
these states at heterointerfaces, the latter caused by chemical bonds
anisotropy. A theory of magneto-induced reflection and transmission of light
through the quantum wells for the light-hole-to-electron absorption edge is
also presented.
