On Hardy-sobolev Embedding
نویسنده
چکیده
1. Interpolation inequalities. A classical problem in analysis is to understand how “smoothness” controls norms that measure the “size” of functions. Maz’ya recognized in his classic text on Sobolev spaces the intrinsic importance of inequalities that would refine both Hardy’s inequality and Sobolev embedding. Dilation invariance and group symmetry play an essential role in determining sharp constants. Recent interest has focused on how to add “error terms” to the classical estimates. The objective here is the following theorem drawn as a novel consequence of this effort to extend Sobolev embedding. Theorem 1. For f ∈ S(Rn), n ≥ 3 and 2 < q ≤ q∗ = 2n n−2
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