Improved Hardy-Sobolev inequalities

Details Improved Hardy-Sobolev inequalities Improved Hardy-Sobolev inequalities

2007-10-21

arxiv.org/abs/0710.3936v1

Mathematics

Spectral Theory

Scientific paper

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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