Beurling–Ahlfors transform constant

Upper bound, last-listed row

| $1.575$ | [BJ2008] | Bañuelos–Janakiraman proved $\lVert B\rVert_p \le 1.575(p^*-1)$ for all $1<p<\infty$. [BJ2008-abs-ub1575] |

exact pinned row

| $1.575$ | <a href="#BJ2008">[BJ2008]</a> | Bañuelos–Janakiraman proved $\lVert B\rVert_p \le 1.575(p^*-1)$ for all $1<p<\infty$. <a href="#BJ2008-abs-ub1575">[BJ2008-abs-ub1575]</a> |

tracked since 2026-07-24 — no movement seen yet

Lower bound, last-listed row

| $1$ | [Leh1965] | Lehto proved $\lVert B\rVert_p \ge p^*-1$, which implies $C_{54}\ge 1$. [BJ2008-Lehto-lb] |

exact pinned row

| $1$ | <a href="#Leh1965">[Leh1965]</a> | Lehto proved $\lVert B\rVert_p \ge p^*-1$, which implies $C_{54}\ge 1$. <a href="#BJ2008-Lehto-lb">[BJ2008-Lehto-lb]</a> |

tracked since 2026-07-24 — no movement seen yet

Checked against material for its cited source

• The row shown above: bound row $1.575$ line 56 citing [BJ2008] — the claim we checked: that Bañuelos and Janakiraman prove the p-norm of the operator B is at most 1.575 times (p* − 1) for every p strictly between 1 and infinity, as the row's comment says. The row's second link, [BJ2008-abs-ub1575], is checked only for whether it points at that statement. What we read supports it: the paper's Theorem 1.2 states the bound with the constant 1.575 for every p between 1 and infinity, and the abstract, where the row's second link points, states the same estimate. This verdict does not cover the correctness of the proof, which includes a numerical bound on a maximum. source link (read in the cited Transactions of the AMS edition, all ten pages (3603–3612) as page images, from an Internet Archive capture dated 2024-03-29 of the PDF at the AMS's /journals/tran/ address; the entry links a /tran/ address, and the AMS site itself answered 403 with a bot challenge at both). About the reference itself, not the bound: The article's first page gives its pages as 3603–3612, and its last page is numbered 3612; the table's reference entry for [BJ2008] gives 3603–3613, as does Crossref's record for the article. Selected: drawn by its position in the list of cited rows, not because it looked wrong.

1 bound row(s) here have been checked against material for their cited source (1 drawn by position, 0 chosen because something already looked wrong). Across this whole ledger 70 row(s) have been drawn by position, against 691 rows that name a source, counted on 2026-09-27: 64 were checked against material for their cited sources and for 6 the cited source could not be read at all. 5 more were chosen for suspicion and checked; they are counted apart, because a set selected for suspicion carries no rate. A row not listed here has NOT been checked.