- Tytuł:
- A Fourier analytical characterization of the Hausdorff dimension of a closed set and of related Lebesgue spaces
- Autorzy:
-
Triebel, Hans
Winkelvoss, Heike - Powiązania:
- https://bibliotekanauki.pl/articles/1221048.pdf
- Data publikacji:
- 1996
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Hausdorff dimension
Hausdorff measure
function spaces - Opis:
- Let Γ be a closed set in $ℝ^n$ with Lebesgue measure |Γ| = 0. The first aim of the paper is to give a Fourier analytical characterization of Hausdorff dimension of Γ. Let 0 < d < n. If there exist a Borel measure µ with supp µ ⊂ Γ and constants $c_{1} > 0$ and $c_{2} > 0$ such that $c_{1}r^{d} ≤ µ (B(x,r)) ≤ c_{2}r^{d}$ for all 0 < r < 1 and all x ∈ Γ, where B(x,r) is a ball with centre x and radius r, then Γ is called a d-set. The second aim of the paper is to provide a link between the related Lebesgue spaces $L_{p}(Γ)$, 0 < p ≤ ∞, with respect to that measure µ on the hand and the Fourier analytically defined Besov spaces $B^s_{p,q}(ℝ^n)$ (s ∈ ℝ, 0 < p ≤ ∞, 0 < q ≤ ∞) on the other hand.
- Źródło:
-
Studia Mathematica; 1996, 121, 2; 149-166
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł