Improved Hardy-sobolev Inequalities
نویسنده
چکیده
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 := x · ∇ and the analysis requires the determination of the operator semigroup {e−tL∗L}t>0 and its properties.
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