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.
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