Open Access
2008 On inequalities of Hardy-Sobolev type
A. Balinsky, W. D. Evans, D. Hundertmark, R. T. Lewis
Banach J. Math. Anal. 2(2): 94-106 (2008). DOI: 10.15352/bjma/1240336296


Hardy-Sobolev-type inequalities associated with the operator $L:=\textbf{{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 $\{e^{-tL^{*}L}\}_{0\neq t \geq 0}.$


Download Citation

A. Balinsky. W. D. Evans. D. Hundertmark. R. T. Lewis. "On inequalities of Hardy-Sobolev type." Banach J. Math. Anal. 2 (2) 94 - 106, 2008.


Published: 2008
First available in Project Euclid: 21 April 2009

zbMATH: 1158.46022
MathSciNet: MR2436870
Digital Object Identifier: 10.15352/bjma/1240336296

Primary: 46E35
Secondary: 35K05

Keywords: Hardy's inequality , heat semigroup , Ledoux's inequality , Sobolev's inequality

Rights: Copyright © 2008 Tusi Mathematical Research Group

Vol.2 • No. 2 • 2008
Back to Top