Generalized Hausdorff dimension distortion in Euclidean spaces under Sobolev mappings

We investigate how the integrability of the derivatives of Orlicz-Sobolev mappings defined on open subsets of ${\mathbb{R}}^n$ affect the sizes of the images of sets of Hausdorff dimension less than $n$. We measure the sizes of the image sets in terms of generalized Hausdorff measures.