Volume 37 • Number 4 • 2014   • Stronger Version of Denjoy-Type Inequality A. Dzhalilov, M. S. M. Noorani and H. Akhadkulov Abstract. Let $f$ be an orientation-preserving circle diffeomorphism with irrational rotation number and $\log f'$ be absolutely continuous, $f''/f'\in L_{p},$ $p>1.$ By using the ratio distortion approach, we prove a sharper result for the key estimate of the Y. Katznelson and D. Ornstein theorem on the absolute continuity of the conjugacy for such circle diffeomorphism $f$. 2010 Mathematics Subject Classification: 37E10, 37C15, 37C40 Full text: PDF