IJPAM: Volume 25, No. 1 (2005)

A GENERALIZED HARDY INEQUALITY TO
THE BAOUENDI-GRUSHIN TYPE OPERATOR

Haifeng Liu$^1$, Pengcheng Niu$^2$
$^{1,2}$Department of Applied Mathematics
Northwestern Polytechnical University
No. 127, Youyi Road, Xi'an, 710072, P.R. CHINA
$^1$e-mail: hfeng_l@yahoo.com
$^2$e-mail: Pengchengniu@yahoo.com


Abstract.By choosing the appropriate test functions and using an inequality on $N$-dimensional vector, a generalized Hardy type inequality with singular weight to the degenerate elliptic operators $\mathcal{L}=\sum_{j=1}^NX_j^2$ generated by the Baouendi-Grushin type vector fields $X_1=\frac{\partial}{\partial
x_1},\cdots,X_k=\frac{\partial}{\partial
x_d},Y_...
...ial}{\partial
y_1},\cdots,Y_k=\vert x\vert^\alpha\frac{\partial}{\partial y_k}$ $(\alpha>0),$ is proved, which generalizes the related results in previous literature.

Received: August 10, 2005

AMS Subject Classification: 26D10, 43A85, 35J70

Key Words and Phrases: degenerate equation, Grushin type operator, Hardy inequality

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 25
Issue: 1