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arXiv · 1403.0215

Hardy Type Inequalities for $\Delta_\lambda$-Laplacians

A. E. Kogoj·S. Sonner
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Abstract

We derive Hardy type inequalities for a large class of sub-elliptic operators that belong to the class of $\Delta_\lambda$-Laplacians and find explicit values for the constants involved. Our results generalize previous inequalities obtained for Grushin type operators $$ \Delta_{x}+ |x|^{2\alpha}\Delta_{y},\qquad\ (x,y)\in\mathbb{R}^{N_1}\times\mathbb{R}^{N_2},\ \alpha\geq 0, $$ which were proved to be sharp.

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A. E. Kogoj, S. Sonner. 2014-03-02. Hardy Type Inequalities for $\Delta_\lambda$-Laplacians. https://arxiv.org/abs/1403.0215

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