  The star-formation rates and the stellar masses of the host galaxies of AGNs
at high-redshifts are keys to understanding the evolution of the relation
between the mass of the spheroidal component of a galaxy and the mass of its
central black hole. We investigate the host galaxies of 31 AGNs with
spectroscopic redshifts between 2 and 4 found in the deep Chandra surveys of
the GOODS fields with the ACS images. The sample can be divided into 17
``extended'' AGNs and 14 ``compact'' AGNs based on the concentration parameter
defined as the difference between the aperture magnitudes with 0.07" and 0.25"
diameter. We derive upper limits of the UV luminosities of the host galaxies of
the ``compact'' AGN sample, and upper and lower limits of the UV luminosities
of the host galaxies of the ``extended'' AGN sample.These limits are consistent
with the knee of the luminosity function of the Lyman Break Galaxies (LBGs) at
z=3, suggesting moderate star-formation rates, less than 40 Msolar/yr, in the
host galaxies of the AGNs at 2<z_sp<4 without correcting the dust extinction.
By combining the limits of the UV luminosities with the observed K-band
magnitudes for the ``extended'' AGNs, we derive the upper and lower limits of
the stellar masses of their host galaxies. The derived upper limits on the
stellar masses range from 10^10 Msolar to 10^12 Msolar. The upper limits imply
that the Mbulge-MBH relation of the high-redshift AGNs is different from that
of the galaxies in the nearby universe or the average Eddington ratio of the
high-redshift AGNs is higher than that of low-redshift AGNs with
lower-luminosity.
