  We present near-infrared imaging with ESO VLT+ISAAC of the host galaxies of
low luminosity quasars in the redshift range 1 < z < 2, aimed at investigating
the relationship between the nuclear and host galaxy luminosities at high
redshift. This work complements our previous study to trace the cosmological
evolution of the host galaxies of high luminosity quasars (Falomo et al. 2004).
The new sample includes 15 low luminosity quasars, nine radio-loud (RLQ) and
six radio-quiet (RQQ). They have similar distribution of redshift and optical
luminosity, and together with the high luminosity quasars they cover a large
range (~4 mag) of the quasar luminosity function. The host galaxies of both
types of quasars are in the range of massive inactive ellipticals between L*
and 10 L*. RLQ hosts are systematically more luminous than RQQ hosts by a
factor of ~2. This difference is similar to that found for the high luminosity
quasars. This luminosity gap appears to be independent of the rest-frame U-band
luminosity but clearly correlated with the rest-frame R-band luminosity. The
color difference between the RQQs and the RLQs is likely a combination of an
intrinsic difference in the strength of the thermal and nonthermal components
in the SEDs of RLQs and RQQs, and a selection effect due to internal dust
extinction. For the combined set of quasars, we find a reasonable correlation
between the nuclear and the host luminosities. This correlation is less
apparent for RQQs than for RLQs. If the R-band luminosity is representative of
the bolometric luminosity, and assuming that the host luminosity is
proportional to the black hole mass, as observed in nearby massive spheroids,
quasars emit with a relatively narrow range of power with respect to their
Eddington luminosity and with the same distribution for RLQs and RQQs.
