Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 41, 2016, 85-102

GENERALIZED DIMENSION ESTIMATES FOR IMAGES OF POROUS SETS IN METRIC SPACES

Aapo Kauranen

University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35 (MaD), FI-40014 University of Jyväskylä, Finland; aapo.p.kauranen 'at' jyu.fi

Abstract. In Q-Ahlfors regular metric measure spaces we obtain essentially sharp dimension estimates for images of porous sets under Hajlasz-type Sobolev maps with L^Q-gradient. The estimates generalize the previous results of Jones and Makarov [7] and Kauranen and Koskela [8].

2010 Mathematics Subject Classification: Primary 30L99, 26B35, 28A78.

Key words: Metric spaces, Sobolev spaces, Hausdorff measure, modulus of continuity.

Reference to this article: A. Kauranen: Generalized dimension estimates for images of porous sets in metric spaces. Ann. Acad. Sci. Fenn. Math. 41 (2016), 85-102.

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doi:10.5186/aasfm.2016.4107