Degenerate P-laplacian Operators on H-type Groups and Applications to Hardy Type Inequalities
نویسندگان
چکیده
Abstract. Let G be a step-two nilpotent group of H-type with Lie algebra G = V ⊕ t. We define a class of vector fields X = {Xj} on G depending on a real parameter k ≥ 1, and we consider the corresponding p-Laplacian operator Lp,ku = divX(|∇Xu| ∇Xu). For k = 1 the vector fields X = {Xj} are the left invariant vector fields corresponding to an orthonormal basis of V , for k = 2 and G being the Heisenberg group they are introduced by Greiner [12]. In this paper we obtain the fundamental solution for the operator Lp,k and as an application, we get a Hardy type inequality associated with X .
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