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Uniform $ L\sp 2$-weighted Sobolev inequalities

Authors: Filippo Chiarenza and Alberto Ruiz
Journal: Proc. Amer. Math. Soc. 112 (1991), 53-64
MSC: Primary 46E35; Secondary 35J15
MathSciNet review: 1055768
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Abstract: We prove the inequality (1) for weights $ w$ in a class which contains the class $ {J_p},p > (n - 1)/2$, introduced by C. Fefferman and D. H. Phong in studying eigenvalues of Schrödinger operators. In our case, $ C$ is independent of the lower order terms of $ P$. As a consequence we prove unique continuation theorem for solutions of $ \Delta + V,V$ in the same class.

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