Weighted Poincaré inequalities on convex domains

@inproceedings{Chua2010WeightedPI,
  title={Weighted Poincar{\'e} inequalities on convex domains},
  author={Sylbert Danley O. Chua and Richard L. Wheeden},
  year={2010}
}
Let Ω be a bounded open convex set in Rn. Suppose that α ≥ 0, β ∈ R, 1 ≤ p ≤ q < ∞, and 1− n p + n q , 1− n + β p + n + α q ≥ 0. Let ρ(x) = dist(x, Ωc) = min{|x − y| : y ∈ Ωc} denote the Euclidean distance to the complement of Ω. Define ρα(Ω) = R Ω ρ(x) αdx, and denote 

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