### Abstract

Let f be an orientation-preserving circle diffeomorphism with irrational rotation number and log f′ be absolutely continuous, f″ / f′ ∈ 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.

Original language | English |
---|---|

Pages (from-to) | 939-948 |

Number of pages | 10 |

Journal | Bulletin of the Malaysian Mathematical Sciences Society |

Volume | 37 |

Issue number | 4 |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

- Circle diffeomorphism
- Conjugating map
- Denjoy inequality
- Rotation number

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Bulletin of the Malaysian Mathematical Sciences Society*,

*37*(4), 939-948.

**Stronger version of denjoy-type inequality.** / Dzhalilov, Akhtam; Md. Noorani, Mohd. Salmi; Akhadkulov, Habibulla.

Research output: Contribution to journal › Article

*Bulletin of the Malaysian Mathematical Sciences Society*, vol. 37, no. 4, pp. 939-948.

}

TY - JOUR

T1 - Stronger version of denjoy-type inequality

AU - Dzhalilov, Akhtam

AU - Md. Noorani, Mohd. Salmi

AU - Akhadkulov, Habibulla

PY - 2014

Y1 - 2014

N2 - Let f be an orientation-preserving circle diffeomorphism with irrational rotation number and log f′ be absolutely continuous, f″ / f′ ∈ Lp, 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.

AB - Let f be an orientation-preserving circle diffeomorphism with irrational rotation number and log f′ be absolutely continuous, f″ / f′ ∈ Lp, 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.

KW - Circle diffeomorphism

KW - Conjugating map

KW - Denjoy inequality

KW - Rotation number

UR - http://www.scopus.com/inward/record.url?scp=84907983739&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907983739&partnerID=8YFLogxK

M3 - Article

VL - 37

SP - 939

EP - 948

JO - Bulletin of the Malaysian Mathematical Sciences Society

JF - Bulletin of the Malaysian Mathematical Sciences Society

SN - 0126-6705

IS - 4

ER -