  The studies of quantum states and optics in a {\it p}-type heterojunction
with lateral surface quantum dot (antidot) superlattice and in the presence of
perpendicular magnetic field are performed. For the first time the Azbel'--
Hofstadter problem is solved for holes in a complicated valence band described
by the $4 \times 4$ Luttinger Hamiltonian. The set of magnetic subbands is
obtained for separate hole levels in a wide interval of magnetic field. We
found remarkable differences between hole spectra and the Hofstadter
"butterfly" for electrons. The influence of the spin-orbit interaction onto
wavefunctions and energy spectrum has been investigated. The probabilities of
optical transitions between quantum states in the valence band and donors
located in the monolayer inside the heterojunction are calculated. The set of
parameters (superlattice periods, amplitude of periodic potential, magnitude of
magnetic field, etc.) required for experimental observation of splitted hole
Landau levels is determined.
