Dimension of images of subspaces under mappings in Triebel‐Lizorkin spaces |
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Authors: | Stanislav Hencl Petr Honzík |
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Affiliation: | Department of Mathematical Analysis, Charles University, Sokolovská 83, Czech Republic |
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Abstract: | Let and let be a ‐quasicontinuous representative of a mapping in the Triebel‐Lizorkin space . We find an optimal value of such that for a.e. the Hausdorff dimension of is at most α. We construct examples to show that the value of β is optimal and we show that it does not increase once p goes below the critical value α. |
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Keywords: | Sobolev mapping Hausdorff dimension 46E35 28A78 |
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