Inégalités à poids pour l'opérateur de Hardy-Littlewood-Sobolev dans les espaces métriques mesurés à deux demi-dimensions
On a metric measure space (X,ϱ,μ), consider the weight functions if ϱ(x,z₀) < 1, if ϱ(x,z₀) ≥ 1, if ϱ(x,z₀) < 1, if ϱ(x,z₀) ≥ 1, where z₀ is a given point of X, and let be an operator kernel satisfying for all x,y ∈ X such that ϱ(x,y) < 1, 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...