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Title: Sobolev interpolation inequalities on generalized John domains
Authors: Chua, S.-K. 
Keywords: δ-balls
Boman domains
Poincaré inequalities
Issue Date: Oct-2009
Citation: Chua, S.-K. (2009-10). Sobolev interpolation inequalities on generalized John domains. Pacific Journal of Mathematics 242 (2) : 215-258. ScholarBank@NUS Repository.
Abstract: We obtain weighted Sobolev interpolation inequalities on generalized John domains that include John domains (bounded or unbounded) for δ-doubling measures satisfying a weighted Poincaré inequality. These measures include ones arising from power weights d(χ, ∂Ω)α and need not be dou- bling. As an application, we extend the Sobolev interpolation inequalities obtained by Caffarelli, Kohn and Nirenberg. We extend these inequalities to product spaces and give some applications on products R{double-struck}M× RMΩ2 of John domains for Ap(R{double-struck}n × Rm) weights and power weights of the type w(χ, y) = dist(χ, G1)α dist(y, G2)β, where G1 ⊂ ∂Ω1 and G2 ⊂ ∂-1.Ω2. For certain cases, we obtain sharp conditions.
Source Title: Pacific Journal of Mathematics
ISSN: 00308730
DOI: 10.2140/pjm.2009.242.215
Appears in Collections:Staff Publications

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