Loomis–Whitney inequalities on corank 1 Carnot groups
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Published:2024-07-01
Issue:2
Volume:49
Page:
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ISSN:2737-114X
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Container-title:Annales Fennici Mathematici
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language:
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Short-container-title:Ann. Fenn. Math.
Abstract
In this paper we provide another way to deduce the Loomis–Whitney inequality on higher dimensional Heisenberg groups \(\mathbb{H}^n\) based on the one on the first Heisenberg group \(\mathbb{H}^1\) and the known nonlinear Loomis–Whitney inequality (which has more projections than ours). Moreover, we generalize the result to the case of corank 1 Carnot groups and products of such groups. Our main tool is the modified equivalence between the Brascamp–Lieb inequality and the subadditivity of the entropy developed in Carlen and Cordero-Erausquin (2009).
Publisher
Finnish Mathematical Society