Loomis–Whitney inequalities on corank 1 Carnot groups

Authors

  • Ye Zhang Okinawa Institute of Science and Technology Graduate University, Analysis on Metric Spaces Unit

Keywords:

Corank 1 Carnot group, Loomis–Whitney inequality, Brascamp–Lieb inequality, entropy, Sobolev inequality, isoperimetric inequality

Abstract

In this paper we provide another way to deduce the Loomis–Whitney inequality on higher dimensional Heisenberg groups Hn based on the one on the first Heisenberg group H1 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).
Section
Articles

Published

2024-07-01

How to Cite

Zhang, Y. (2024). Loomis–Whitney inequalities on corank 1 Carnot groups. Annales Fennici Mathematici, 49(2), 437–459. https://doi.org/10.54330/afm.146800