Inequalities of Brascamp-Lieb type on the Heisenberg group

Kaiyi Huang; Betsy Stovall

Inequalities of Brascamp-Lieb type on the Heisenberg group

Classical Analysis and ODEs 2024-04-09 v2

Authors: Kaiyi Huang , Betsy Stovall

Abstract

We prove both necessary and sufficient conditions for $L^p$ -bound\-ed\-ness of certain multilinear generalized Radon transforms that arise as Heisenberg group analogues of the Brascamp--Lieb inequalities on Euclidean space. The necessary and sufficient conditions coincide in some important special cases, but differ in others.

Keywords

Brascamp-Lieb inequalities Heisenberg group multilinear generalized Radon transforms $L^p$-boundedness harmonic analysis

Cite

@article{arxiv.2401.02510,
  title  = {Inequalities of Brascamp-Lieb type on the Heisenberg group},
  author = {Kaiyi Huang and Betsy Stovall},
  journal= {arXiv preprint arXiv:2401.02510},
  year   = {2024}
}

Comments

We corrected the formulae of conditions (C1) and (C2), modified the statement of Proposition 2.2, and rewrote the proof of Lemma 4.4 for clarity; 13 pages

Inequalities of Brascamp-Lieb type on the Heisenberg group

Abstract

Keywords

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