Publikace na Matematicko-fyzikální fakulta |
2015
Abstrakt
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.