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arXiv · 0710.3936

Improved Hardy-Sobolev inequalities

A. Balinsky·W. D. Evans·D. Hundertmark·R. T. Lewis
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Abstract

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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BibTeXRIS

A. Balinsky, W. D. Evans, D. Hundertmark, R. T. Lewis. 2007-10-21. Improved Hardy-Sobolev inequalities. https://arxiv.org/abs/0710.3936

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