  We investigate effects of lateral confinement on spin splitting of energy
levels in 2D hole gases grown on [311] GaAs. We found that lateral confinement
enhances anisotropy of spin splitting relative to the 2D gas for both confining
directions. Unexpectedly, the effective $g$-factor does not depend on the 1D
energy level number $N$ for $B\|[0\bar{1}1]$ while it has strong $N$-dependence
for $B\|[\bar{2}33]$. Apart from quantitative difference in the spin splitting
of energy levels for the two orthogonal confinement directions we also report
qualitative differences in the appearance of spin-split plateaus, with
non-quantized plateaus observed only for the confinement in $[0\bar{1}1]$
direction. In our samples we can clearly associate the difference with
anisotropy of spin-orbit interactions.
