Dimension of images of subspaces under mappings in Triebel-Lizorkin spaces

Abstrakt

Let m R-k be a s,p-quasicontinuous representative of a mapping in the Triebel-Lizorkin space F-p,q.(s) We find an optimal value of beta(n, m , p ,alpha , s) such that for H-beta a.e. y is an element of(0,1)(n-m) the Hausdorff dimension of f ((0,1)(m) x {y}) is at most alpha. We construct examples to show that the value of beta is optimal and we show that it does not increase once p goes below the critical value alpha.

Klíčová slova

• Sobolev mapping
• Hausdorff dimension