  We analyze a sample of 3300 galaxies between redshifts z~3.5 and z~8.5
selected from JWST images in the Hubble Ultra Deep Field (HUDF) and UKIDSS
Ultra Deep Survey field, including objects with stellar masses as low as ~ 10^8
Msun up to z~8. The depth and wavelength coverage of the JWST data allow us,
for the first time, to derive robust stellar masses for such high-z, low
stellar-mass galaxies on an individual basis. We compute the galaxy stellar
mass function (GSMF), after complementing our sample with ancillary data from
CANDELS to constrain the GMSF at high stellar masses (M > M*). Our results show
a steepening of the low stellar-mass end slope (a) with redshift, with a =
-1.61 (+/-0.05) at z~4 and a = -1.98 (+/-0.14) at z~7. We also observe an
evolution of the normalization phi* from z~7 to z~4, with phi*(z~4)/phi*(z~7)=
130 (+210/-50). Our study incorporates a novel method for the estimation of the
Eddington bias that takes into account its possible dependence both on stellar
mass and redshift, while allowing for skewness in the error distribution. We
finally compute the resulting cosmic stellar mass density and find a flatter
evolution with redshift than previous studies.
