Improved Hardy-Sobolev inequalities

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The main result includes features of a Hardy-type inequality and an inequality of either Sobolev or Gagliardo-Nirenberg type. It is inspired by the method of proof of a recent improved Sobolev inequality derived by M. Ledoux which brings out the connection between Sobolev embeddings and heat kernel bounds. Here Ledoux's technique is applied to the operator $L:= {\bf{x}} \cdot \nabla$ and the analysis requires the determination of the operator semigroup $\{e^{-tL^{*}L}\}_{t>0}$ and its properties.

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Spectral Theory, Mathematical Physics

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http://salesiana.dossiersoluciones.com/handle/123456789/140477

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0710.3936
 http://arxiv.org/abs/0710.3936

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arXiv