Inégalités à poids pour l'opérateur de Hardy-Littlewood-Sobolev dans les espaces métriques mesurés à deux demi-dimensions

• Autorzy: David Mascré
• Języki publikacji: FR EN

Abstrakty

EN

On a metric measure space (X,ϱ,μ), consider the weight functions
$w_{α}(x) = ϱ(x,z₀)^{-α₀}$ if ϱ(x,z₀) < 1,
$w_{α}(x) = ϱ(x,z₀)^{-α₁}$ if ϱ(x,z₀) ≥ 1,
$w_{β}(x) = ϱ(x,z₀)^{-β₀}$ if ϱ(x,z₀) < 1,
$w_{β}(x) = ϱ(x,z₀)^{-β₁}$ if ϱ(x,z₀) ≥ 1,
where z₀ is a given point of X, and let $κ_{a}: X×X → ℝ₊$ be an operator kernel satisfying
$κ_{a}(x,y) ≤ cϱ(x,y)^{a-d}$ for all x,y ∈ X such that ϱ(x,y) < 1,
$κ_{a}(x,y) ≤ cϱ(x,y)^{a-D}$ for all x,y ∈ X such that ϱ(x,y)≥ 1,
where 0 < a < min(d,D), and d and D are respectively the local and global volume growth rate of the space X. We determine conditions on a, α₀, α₁, β₀, β₁ ∈ ℝ for the Hardy-Littlewood-Sobolev operator with kernel $κ(x,y) = w_{β}(x)κ_{a}(x,y)w_{α}(y)$ to be bounded from $L^{p}(X)$ to $L^{q}(X)$ for 1 < p ≤ q < ∞.

Kategorie tematyczne

• 42B35: Function spaces arising in harmonic analysis
• 26A33: Fractional derivatives and integrals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2006
• Tom: 105
• Numer: 1
• Strony: 77-104

Daty

wydano

2006

Twórcy

autor

David Mascré

• Département de Mathématiques, Université de Cergy-Pontoise, 95 302 Cergy-Pontoise Cedex, France

Identyfikatory

DOI

10.4064/cm105-1-9