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Dimension of images of subspaces under mappings in Triebel‐Lizorkin spaces
Author(s) -
Hencl Stanislav,
Honzík Petr
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201300015
Subject(s) - mathematics , linear subspace , hausdorff dimension , dimension (graph theory) , hausdorff space , space (punctuation) , value (mathematics) , packing dimension , pure mathematics , construct (python library) , minkowski–bouligand dimension , mathematical analysis , statistics , fractal dimension , fractal , computer science , programming language , operating system
Let m < α < p and let f : R n → R kbe a s , p ‐quasicontinuous representative of a mapping in the Triebel‐Lizorkin space F p , q s . We find an optimal value of β ( n , m , p , α , s ) such that for H β a.e. y ∈ ( 0 , 1 ) n − mthe Hausdorff dimension of f ( ( 0 , 1 ) m × { y } ) 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.