Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 36, 2011, 553-566

GENERALIZED DIMENSION DISTORTION UNDER MAPPINGS OF SUB-EXPONENTIALLY INTEGRABLE DISTORTION

Tapio Rajala, Aleksandra Zapadinskaya and Thomas Zürcher

University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35, FI-40014 University of Jyväskylä, Finland; tapio.m.rajala 'at' jyu.fi

University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35, FI-40014 University of Jyväskylä, Finland; aleksandra.zapadinskaya 'at' jyu.fi

University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35, FI-40014 University of Jyväskylä, Finland; thomas.t.zurcher 'at' jyu.fi

Abstract. We prove a dimension distortion estimate for mappings of sub-exponentially integrable distortion in Euclidean spaces, which is sharp modulo a constant.

2010 Mathematics Subject Classification: Primary 30C62.

Key words: Mappings of finite distortion, sub-exponential distortion, generalized Hausdorff measure, Hausdorff dimension.

Reference to this article: T. Rajala, A. Zapadinskaya and T. Zürcher: Generalized dimension distortion under mappings of sub-exponentially integrable distortion. Ann. Acad. Sci. Fenn. Math. 36 (2011), 553-566.

Full document as PDF file

doi:10.5186/aasfm.2011.3631