DOIAbstract
We prove various Hardy-type and uncertainty inequalities on a stratified Lie group G. In particular, we show that the operators Tα:f-αL-α/2f, where || is a homogeneous norm, 0<α<Q/p, and L is the sub-Laplacian, are bounded on the Lebesgue space Lp(G). As consequences, we estimate the norms of these operators sufficiently precisely to be able to differentiate and prove a logarithmic uncertainty inequality. We also deduce a general version of the Heisenberg-Pauli-Weyl inequality, relating the Lp norm of a function f to the Lq norm of ||βf and the Lr norm of Lδ/2f
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