Inequalities of Hardy-Sobolev type in Carnot-Carathéodory spaces

2008/04/17 by Danielli, Donatella, Garofalo, Nicola, Phuc, Nguyen Cong · 1 citation
#26D10 #35H20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0804.2833

Abstract

We consider various types of Hardy-Sobolev inequalities on a Carnot-Carathéodory space (\Om, d) associated to a system of smooth vector fields X=\X₁, X₂,...,X_m\ on \RRⁿ satisfying the Hörmander's finite rank condition rank Lie[X₁,...,X_m] ≡ n. One of our main concerns is the trace inequality ∫_\Om|ϕ(x)|^pV(x)dx≤ C∫_\Om|Xϕ|^pdx, ϕ∈ C^∞₀(\Om), where V is a general weight, i.e., a nonnegative locally integrable function on \Om, and 1

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• A Reshetnyak type theorem for quasiregular values on Carnot groups of H-type

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