Hardy inequalities related to Grushin type operators

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Hardy-type inequalities related to degenerate elliptic differential operators (2006, methodology): “6) is already obtained in the case 1 < p < Q by the author in [18].”
On a semilinear elliptic equation in Hn (2008, background): “RN u2 |y|2 (a Hardy type inequality, see [12]) and the easy-to-check identity”
Hardy's inequality for fractional powers of the sublaplacian on the Heisenberg group (2015, background): “We also refer the reader to [3, 7, 15, 22] concerning several kinds of inequalities related to either the Grushin operator, or in Carnot–Carathéodory spaces, or on the Heisenberg group.”
Double phase transonic flow problems with variable growth: nonlinear patterns and stationary waves (2019, result): “d bounds in the calculus of variations. In [10] Caﬀarelli, Kohn and Nirenberg proved a rather general interpolation inequality with weights, which extends the Hardy-Littlewood inequality. We refer to [2, 15, 22] for related inequalities in the context of Grushin-type operators. In this section, moti”