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 $\{e^{-tL^{*}L}\}_{0\neq t \geq 0}.$
Banach J. Math. Anal.
2(2):
94-106
(2008).
DOI: 10.15352/bjma/1240336296