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.
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