Year: 2026
Type: preprint
Abstract: We show that the strong maximal operator on ${\mathbb R}^2$ does not satisfy a linear weighted $L^2$ estimate in terms of the rectangular $A_2$ characteristic. More precisely, we construct weights with arbitrarily large characteristic for which the operator norm is bounded below by $[w]_{A_2^{\mathrm{str}}}\sqrt{\log [w]_{A_2^{\mathrm{str}}}}$. The proof is elementary. It uses an explicit two-parameter mass recurrence on a product of geometric interval partitions, together with a direct comparison of arbitrary rectangular averages with anchored averages.
Source: arXiv (Cornell University)
Author: Lerner, Andrei K.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213252301