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arXiv · 2503.15656

Finiteness of the H\"{o}lder-Brascamp-Lieb Constant Revisited

Philip T. Gressman
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Abstract

Abstract H\"{o}lder-Brascamp-Lieb inequalities have become a ubiquitous tool in Fourier analysis in recent years, due in large part to a theorem of Bennett, Carbery, Christ, and Tao (2008,2010) characterizing finiteness of the H\"{o}lder-Brascamp-Lieb constant. Here we provide a new characterization of a substantially different nature involving directed graphs of subspaces. Its practical value derives from its complementary nature to the Bennett, Carbery, Christ, and Tao conditions: it creates a means by which one can establish finiteness of the H\"{o}lder-Brascamp-Lieb constant by analysis of a well-chosen, finite list of subspaces rather than by checking conditions on all subspaces of the underlying vector space. The proof is elementary and is essentially an "explicitization" of the semi-explicit factorization algorithm of Carbery, H\"{a}nninen, and Valdimarsson (2023).

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Philip T. Gressman. 2025-03-19. Finiteness of the H\"{o}lder-Brascamp-Lieb Constant Revisited. https://arxiv.org/abs/2503.15656

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