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The role of conformal anomaly in AdS/CFT and related issues is clarified. Thecomparison of holographic and QFT conformal anomalies (with account of branequantum gravity contribution) indicates on the possibility for brane quantumgravity to occur within AdS/CFT set-up. 3d quantum induced inflationary (orhyperbolic) brane-world is shown to be realized in frames of AdS3/CFT2correspondence where the role of 2d brane cosmological constant is played byeffective tension due to two-dimensional conformal anomaly. The dynamicalequations to describe 4d FRW-Universe with account of quantum effects producedby conformal anomaly are obtained. The quantum corrected energy, pressure andentropy are found. Dynamical evolution of entropy bounds in inflationaryUniverse is estimated and its comparison with quantum corrected entropy isdone. It is demonstrated that entropy bounds for quantum corrected entropy aregetting the approximate ones and occur for some limited periods of evolution ofinflationary Universe.Comment: LaTeX file, 21 page

AdS/CFT CORRESPONDENCE, CONFORMAL ANOMALY AND QUANTUM CORRECTED ENTROPY BOUNDS