Finiteness of the Hölder-Brascamp-Lieb Constant Revisited
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915206271074304 |
|---|---|
| author | Gressman, Philip T. |
| author_facet | Gressman, Philip T. |
| contents | Abstract Hölder-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 Hölder-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 Hölder-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, Hänninen, and Valdimarsson (2023). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15656 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finiteness of the Hölder-Brascamp-Lieb Constant Revisited Gressman, Philip T. Classical Analysis and ODEs Abstract Hölder-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 Hölder-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 Hölder-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, Hänninen, and Valdimarsson (2023). |
| title | Finiteness of the Hölder-Brascamp-Lieb Constant Revisited |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2503.15656 |