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1. CJM 2010 (vol 62 pp. 1116)

Jin, Yongyang; Zhang, Genkai
 Degenerate p-Laplacian Operators and Hardy Type Inequalities on H-Type Groups Let \$\mathbb G\$ be a step-two nilpotent group of H-type with Lie algebra \$\mathfrak G=V\oplus \mathfrak t\$. We define a class of vector fields \$X=\{X_j\}\$ on \$\mathbb G\$ depending on a real parameter \$k\ge 1\$, and we consider the corresponding \$p\$-Laplacian operator \$L_{p,k} u= \operatorname{div}_X (|\nabla_{X} u|^{p-2} \nabla_X u)\$. For \$k=1\$ the vector fields \$X=\{X_j\}\$ are the left invariant vector fields corresponding to an orthonormal basis of \$V\$; for \$\mathbb G\$ being the Heisenberg group the vector fields are the Greiner fields. In this paper we obtain the fundamental solution for the operator \$L_{p,k}\$ and as an application, we get a Hardy type inequality associated with \$X\$. Keywords:fundamental solutions, degenerate Laplacians, Hardy inequality, H-type groupsCategories:35H30, 26D10, 22E25

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