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Estimates for $L^p$ variants of Gowers norms — arXiv:2609.08916

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.08916
License (as archived): CC0-1.0
Archived: 2026-10-16T14:49:31.557Z
SHA-256 of the archived text: b0107eb7542645de08c7346669b28eadd8aae210a1bc4bac1ab3361270a6192b
Stable URL of this page: https://metraipolis.com/documento/dc_ebb643c5abeb

How to cite

Estimates for $L^p$ variants of Gowers norms — arXiv:2609.08916 — arXiv (en), https://arxiv.org/abs/2609.08916 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ebb643c5abeb (Metraipolis archive dc_ebb643c5abeb, sha256 b0107eb7542645de08c7346669b28eadd8aae210a1bc4bac1ab3361270a6192b)

BibTeX

@misc{dcebb643c5abeb,
  title = {Estimates for $L^p$ variants of Gowers norms — arXiv:2609.08916},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.08916},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ebb643c5abeb; sha256 b0107eb7542645de08c7346669b28eadd8aae210a1bc4bac1ab3361270a6192b},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.08916. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Motivated by a log-convexity question of Bennett and Tao, we consider Gowers-type functionals defined by $L^p$ norms of multiple autocorrelations. We prove sharp bounds in terms of $L^q$ norms and characterise the near-extremisers on Euclidean spaces as well as locally compact abelian groups. We also establish two families of degree-lowering inequalities and study their near-extremisers. As a byproduct of this broader theory, we show that the constant in the log-convexity estimate for Gowers norms is strictly less than unity, confirming the aforementioned conjecture of Bennett and Tao. Finally, we characterise the $p$ for which the Gowers-type functionals necessarily satisfy the triangle inequality on nonnegative measurable functions.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-09 in math.CO).
Categorie arXiv: Classical Analysis and ODEs (math.CA) ; Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2609.08916 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T14:32:29.957Z dalla pagina https://arxiv.org/catchup/math.CO/2026-09-09?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).