Photoluminescence properties of the low-dimensional semiconductor nanostructures of materials with indirect electronic band gap are studied theoretically with an emphasis put on the coupling of charge carriers to the atomic lattice vibrations. The photoluminescence intensity decay time dependence, the temperature dependence of the photoluminescence as well as the dependence of the photoluminescence on the lateral dimensions of the nanoparticles are considered theoretically together with their comparison with experimental data. These properties are treated using the example of the photoluminescence properties of small InAs nanoparticles. The results obtained for the small particles of InAs are expected to be interesting also in connection with the properties of e. g. silicon nanostructures.