The role of conformal anomaly in AdS/CFT and related issues is clarified. T
he comparison of holographic and QFT conformal anomalies (with the account
of brane quantum gravity contribution) indicates the possibility for brane
quantum gravity to occur within the AdS/CFT setup. Three-dimensional quantu
m induced inflationary (or hyperbolic) brave-world is shown to be realized
in the frames of AdS3/CFT2 correspondence where the role of 2d brane cosmol
ogical constant is played by effective tension due to two-dimensional confo
rmal anomaly. The dynamical equations to describe 4d FRW universe with the
account of quantum effects produced by conformal anomaly are obtained. The
quantum corrected energy, pressure and entropy are found. The dynamical evo
lution of entropy bounds in the inflationary universe is estimated and its
comparison with quantum corrected entropy is done. It is demonstrated that
entropy bounds for quantum corrected entropy are getting the approximate on
es and occur for some limited periods of evolution of the inflationary univ
erse.