Brascamp--Lieb inequalities on locally compact abelian groups

2024/12/16 by Bennett, Jonathan, Cowling, Michael G.
#22D05 #44A12 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2412.11514

Abstract

We establish a structure theorem for the Brascamp--Lieb constant formulated in the general setting of locally compact abelian groups. This extends and unifies the finiteness characterisations previously known for euclidean spaces and for finitely generated groups and their duals. We place particular emphasis on Fourier invariance throughout, reflecting the fundamental Fourier invariance of Brascamp--Lieb multilinear forms in this context.

Related

• Fourier duality in the Brascamp-Lieb inequality
• The optimal constants in Holder-Brascamp-Lieb inequalities for discrete Abelian groups
• On Holder-Brascamp-Lieb inequalities for torsion-free discrete Abelian\n groups
• Finiteness of the Hölder-Brascamp-Lieb Constant Revisited
• The nonlinear Brascamp-Lieb inequality for simple data