On Hardy-Sobolev embedding

Details On Hardy-Sobolev embedding On Hardy-Sobolev embedding

2009-07-22

arxiv.org/abs/0907.3932v1

Mathematics

Analysis of PDEs

7 pages, AMSLaTex

Scientific paper

Linear interpolation inequalities that combine Hardy's inequality with sharp Sobolev embedding are obtained using classical arguments of Hardy and Littlewood (Bliss lemma). Such results are equivalent to Caffarelli-Kohn-Nirenberg inequalities with sharp constants. A one-dimensional convolution inequality for the exponential density is derived as an application of these methods.

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