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

Anisotropic modification of the effective hole $g$-factor by electrostatic confinement