  We have calculated the density-density (Lindhard) response function of a
homogeneous two-dimensional (2D) hole gas in the static (omega=0) limit. The
bulk valence-band structure comprising heavy-hole (HH) and light-hole (LH)
states is modeled using Luttinger's kdotp approach within the axial
approximation. We elucidate how, in contrast to the case of conduction
electrons, the Lindhard function of 2D holes exhibits unique features
associated with (i) the confinement-induced HH-LH energy splitting and (ii) the
HH-LH mixing arising from the charge carriers' in-plane motion. Implications
for the dielectric response and related physical observables are discussed.
