Geodesic
SOME HARDY-TYPE INEQUALITIES FOR THE GENERALIZED BAOUENDI-GRUSHIN OPERATORS
Glasgow mathematical journal, Tome 46 (2004) no. 3, pp. 515-527

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DOI

In this paper, we prove some Hardy-type inequalities for the degenerate operators, $L_{p,\alpha}u\,{=}\,{\rm div}_L(|\nabla_Lu|^{p-2}\nabla_Lu)$, where $\nabla_Lu\,{=}\,(\frac{\partial u}{\partial z_1},\ldots,\frac{\partial u}{\partial z_n},|z|^\alpha \frac{\partial u}{\partial t_1},\ldots,|z|^\alpha\frac{\partial u}{\partial t_m})$. These inequalities are established for the whole space, the pseudo-ball and the external domain of the pseudo-ball. We also give a generalization of a result in [8]. Finally, a sharp inequality for $L_{\alpha}\,{=}\,L_{2,\alpha}$ is obtained.
DOI : 10.1017/S0017089504002034
Mots-clés : 35H20, 47F05 
NIU, PENGCHENG; CHEN, YANXIA; HAN, YAZHOU. SOME HARDY-TYPE INEQUALITIES FOR THE GENERALIZED BAOUENDI-GRUSHIN OPERATORS. Glasgow mathematical journal, Tome 46 (2004) no. 3, pp. 515-527. doi: 10.1017/S0017089504002034
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     title = {SOME {HARDY-TYPE} {INEQUALITIES} {FOR} {THE} {GENERALIZED} {BAOUENDI-GRUSHIN} {OPERATORS}},
     journal = {Glasgow mathematical journal},
     pages = {515--527},
     year = {2004},
     volume = {46},
     number = {3},
     doi = {10.1017/S0017089504002034},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089504002034/}
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