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- W2023180310 abstract "Let S be a semi direct product $S=Nrtimes A$ where N is a connected and simply connected, non-abelian, nilpotent meta-abelian Lie group and A is isomorphic with ℝ k , k > 1. We consider a class of second order left-invariant differential operators on S of the form $mathcal{L}_alpha=L^a+Delta_alpha,$ where α ∈ ℝ k , and for each a ∈ ℝ k , L a is left-invariant second order differential operator on N and $Delta_alpha=Delta-langlealpha,nablarangle,$ where Δ is the usual Laplacian on ℝ k . Using some probabilistic techniques (skew-product formulas for diffusions on S and N respectively, the concept of the derivative of a measure, etc.) we obtain an upper bound for the derivatives of the Poisson kernel for $mathcal{L}_alpha.$ During the course of the proof we also get an upper estimate for the derivatives of the transition probabilities of the evolution on N generated by L σ(t), where σ is a continuous function from [0, ∞ ) to ℝ k ." @default.
- W2023180310 created "2016-06-24" @default.
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- W2023180310 date "2013-08-30" @default.
- W2023180310 modified "2023-09-27" @default.
- W2023180310 title "Estimates for the Derivatives of the Poisson Kernel on Nilpotent Meta-Abelian Groups" @default.
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- W2023180310 doi "https://doi.org/10.1007/s11118-013-9368-3" @default.
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