Journal
ADVANCES IN MATHEMATICS
Volume 277, Issue -, Pages 365-387Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2014.12.040
Keywords
Stratified group; Uncertainty principle; Hardy's inequality; Heisenberg's inequality
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Funding
- Australian Research Council [DP110102488]
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We prove various Hardy-type and uncertainty inequalities on a stratified Lie group G. In particular, we show that the operators T-alpha : f -> |center dot|(-alpha) L(-alpha/2)f, where |center dot| is a homogeneous norm, 0 < alpha < Q/p, and L is the sub-Laplacian, are bounded on the Lebesgue space L-P(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 L-P norm of a function f to the L-q norm of |center dot|(beta) f and the L-r norm of L(delta/2)f. (C) 2015 Elsevier Inc. All rights reserved.
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