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Zbl 1158.46022
Balinsky, A.; Evans, W.D.; Hundertmark, D; Lewis, R.T.
On inequalities of Hardy-Sobolev type.
(English)
[J] Banach J. Math. Anal. 2, No. 2, 94-106, electronic only (2008). ISSN 1735-8787/e

Summary: Hardy-Sobolev-type inequalities associated with the operator $L := {\bold x}\cdot\nabla$ are established, using an improvement to the Sobolev embedding theorem obtained by M. Ledoux. The analysis involves the determination of the operator semigroup $\{e^-{tL^*L}\}_{t>0}$.
MSC 2000:
*46E35 Sobolev spaces and generalizations
26D10 Inequalities involving derivatives, diff. and integral operators
26D15 Inequalities for sums, series and integrals of real functions
47D06 One-parameter semigroups and linear evolution equations

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