  We constrain the behavior of the radio luminosity function (RLF) of two
classes of active galactic nuclei (AGN) namely AGN of low radio power (LRP) and
BL Lac objects. The extrapolation of the observed steep RLFs to low power
predicts a space density of such objects that exceeds that of the sources that
can harbor them and this requires a break to a shallower slope. For LRP AGN we
obtain P_br,LRP > 10^20.5 W/Hz at 1.4 GHz to limit their density to be smaller
than that of elliptical galaxies with black hole masses M_BH > 10^7.5 solar
masses. By combining this value with the limit derived by the observations the
break must occur at P_br,LRP~10^20.5-10^21.5 W/Hz. For BL Lacs we find
P_br,BLLAC > 10^23.3 W/Hz otherwise they would outnumber the density of
weak-lined and compact radio sources, while the observations indicate
P_br,BLLAC < 10^24.5 W/Hz. In the framework of the AGN unified model a low
luminosity break in the RLF of LRP AGN must correspond to a break in the RLF of
BL Lacs. The ratio between P_br,LRP and P_br,BLLAC is ~10^3, as expected for a
jet Doppler factor of ~10.
