DIMENSION DISTORTION OF IMAGES OF SETS UNDER SOBOLEV MAPPINGS

被引：6

作者：

Hencl, Stanislav ^{[1
]}

Honzik, Petr ^{[1
]}

机构：

[1] Charles Univ Prague, Dept Math Anal, Prague 18600 8, Czech Republic

来源：

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA | 2015年 / 40卷 / 01期

关键词：

Sobolev mapping; Hausdorff dimension; QUASI-CONFORMAL MAPPINGS; FREQUENCY; SUBSPACES; SPACES;

D O I：

10.5186/aasfm.2015.4026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let f: R-n -> R-k be a continuous representative of a mapping in a Sobolev space W-1,W-P, p > n. Suppose that the Hausdorff dimension of a set M is at most alpha. Kaufmann [12] proved an optimal bound beta = p alpha/p-n+alpha for the dimension of the image of M under the mapping f. We show that this bound remains essentially valid even for 1 < p <= n and we also prove analogous bound for mappings in Sobolev spaces with higher order or even fractional smoothness.

引用

页码：427 / 442

页数：16

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