On Fourier asymptotics of a generalized Cantor measure

• Autorzy: Bérenger Akon Kpata , Ibrahim Fofana , Konin Koua
• Języki publikacji: EN

Abstrakty

EN

Let d be a positive integer and μ a generalized Cantor measure satisfying $μ = ∑_{j = 1}^{m} a_{j}μ∘S_{j}^{-1}$, where $0 < a_{j} < 1$, $∑_{j = 1}^{m}a_{j} = 1$, $S_{j} = ρR + b_{j}$ with 0 < ρ < 1 and R an orthogonal transformation of $ℝ^{d}$. Then
⎧1 < p ≤ 2 ⇒
⎨$sup_{r>0} r^{d(1/α'-1/p')} (∫_{J_{x}^{r}} |μ̂(y)|^{p'}dy)^{1/p'} ≤ D₁ρ^{-d/α'}$, $x ∈ ℝ^{d}$,
⎩ p = 2 ⇒ inf_{r≥1} r^{d(1/α'-1/2)} (∫_{J₀^{r}}|μ̂(y)|² dy)^{1/2} ≥ D₂ρ^{d/α'}$,
where $J_{x}^{r} = ∏_{i=1}^{d} (x_{i} - r/2,x_{i} + r/2)$, α' is defined by $ρ^{d/α'} = (∑_{j=1}^{m} a_{j}^{p})^{1/p}$ and the constants D₁ and D₂ depend only on d and p.

Kategorie tematyczne

• 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
• 28A80: Fractals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 119
• Numer: 1
• Strony: 109-122

Daty

wydano

2010

Twórcy

autor

Bérenger Akon Kpata

• UFR Mathématiques et Informatique, Université de Cocody, 22 BP 582 Abidjan 22, Côte d'Ivoire

autor

Ibrahim Fofana

• UFR Mathématiques et Informatique, Université de Cocody, 22 BP 582 Abidjan 22, Côte d'Ivoire

autor

Konin Koua

• UFR Mathématiques et Informatique, Université de Cocody, 22 BP 582 Abidjan 22, Côte d'Ivoire

Identyfikatory

DOI

10.4064/cm119-1-6