# Generalized dimension compression under mappings of exponentially integrable distortion

Open Mathematics (2011)

- Volume: 9, Issue: 2, page 356-363
- ISSN: 2391-5455

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topAleksandra Zapadinskaya. "Generalized dimension compression under mappings of exponentially integrable distortion." Open Mathematics 9.2 (2011): 356-363. <http://eudml.org/doc/269401>.

@article{AleksandraZapadinskaya2011,

abstract = {We prove a dimension compression estimate for homeomorphic mappings of exponentially integrable distortion via a modulus of continuity result by D. Herron and P. Koskela [Mappings of finite distortion: gauge dimension of generalized quasicircles, Illinois J. Math., 2003, 47(4), 1243–1259]. The essential sharpness of our estimate is demonstrated by an example.},

author = {Aleksandra Zapadinskaya},

journal = {Open Mathematics},

keywords = {Mapping of finite distortion; Exponentially integrable distortion; Generalized Hausdorff measure; Hausdorff dimension; mapping of finite distortion; exponentially integrable distortion; generalized Hausdorff measure},

language = {eng},

number = {2},

pages = {356-363},

title = {Generalized dimension compression under mappings of exponentially integrable distortion},

url = {http://eudml.org/doc/269401},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Aleksandra Zapadinskaya

TI - Generalized dimension compression under mappings of exponentially integrable distortion

JO - Open Mathematics

PY - 2011

VL - 9

IS - 2

SP - 356

EP - 363

AB - We prove a dimension compression estimate for homeomorphic mappings of exponentially integrable distortion via a modulus of continuity result by D. Herron and P. Koskela [Mappings of finite distortion: gauge dimension of generalized quasicircles, Illinois J. Math., 2003, 47(4), 1243–1259]. The essential sharpness of our estimate is demonstrated by an example.

LA - eng

KW - Mapping of finite distortion; Exponentially integrable distortion; Generalized Hausdorff measure; Hausdorff dimension; mapping of finite distortion; exponentially integrable distortion; generalized Hausdorff measure

UR - http://eudml.org/doc/269401

ER -

## References

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- [7] Faraco D., Koskela P., Zhong X., Mappings of finite distortion: the degree of regularity, Adv. Math., 2005, 190(2), 300–318 http://dx.doi.org/10.1016/j.aim.2003.12.009 Zbl1075.30012
- [8] Gehring F.W., The L p-integrability of the partial derivatives of a quasiconformal mapping, Acta Math., 1973, 130(1), 265–277 http://dx.doi.org/10.1007/BF02392268 Zbl0258.30021
- [9] Herron D.A., Koskela P., Mappings of finite distortion: gauge dimension of generalized quasicircles, Illinois J. Math., 2003, 47(4), 1243–1259 Zbl1050.30012
- [10] Koskela P., Zapadinskaya A., Zürcher T., Mappings of finite distortion: generalized Hausdorff dimension distortion, J. Geom. Anal., 2010, 20(3), 690–704 http://dx.doi.org/10.1007/s12220-010-9121-8 Zbl1205.30017
- [11] Rajala T., Zapadinskaya A., Zürcher T., Generalized Hausdorff dimension distortion in Euclidean spaces under Sobolev mappings, preprint available at http://arxiv.org/abs/1007.2091 Zbl1252.46024

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