In this note we revisit the upper endpoint estimates for commutators following the line by Harboure, Segovia, and Torrea [Illinois J. Math.
41 no. 4 (1997), 676–700]. Relying upon the suitable BMO subspace suited
for the commutator that was introduced in Accomazzo’s PhD thesis (2020),
we obtain a counterpart for commutators of the upper endpoint extrapolation
result by Harboure, Mac´ıas and Segovia [Amer. J. Math. 110 no. 3 (1988),
383–397]. Multilinear counterparts are provided as well.
