Generalized Hausdorff dimension distortion in Euclidean spaces under Sobolev mappings

Planar Sobolev Homeomorphisms and Hausdorff Dimension Distortion

We investigate how planar Sobolev-Orlicz homeomorphisms map sets of Hausdorff dimension less than two. With the correct gauge functions the generalized Hausdorff measures of the image sets are shown to be zero.

Connected Mappings of Hausdorff Spaces

Hausdorff Dimension in Convex Bornological Spaces

For non-metrizable spaces the classical Hausdorff dimension is meaningless. We extend the notion of Hausdorff dimension to arbitrary locally convex linear topological spaces, and thus to a large class of non-metrizable spaces. This involves a limiting procedure using the canonical bornological structure. In the case of normed spaces the new notion of Hausdorff dimension is equivalent to the cla...

Function spaces and Hausdorff dimension on fractals

We start by surveying a possible approach for function spaces of Besov type on special closed subsets of Rn. Afterwards we recall that, in the case of Sobolev spaces and Besov spaces on Rn, the Hausdorff dimension for the graphs of continuous functions belonging to such spaces has been studied by several authors, and that in the case of Besov spaces the final answer concerning the maximal possi...

Dimension-free imbeddings of Sobolev spaces

We prove dimension-free imbedding theorems for Sobolev spaces using extrapolation means and the Gross logarithmic inequality.