Author

Cody B. Stockdale

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Preprint Sep 2026

The weak-type (1,1) bound for the Hardy--Littlewood maximal function is $O(\sqrt{n} \log n)$

We prove a weak-type $(1,1)$ estimate for the centered Hardy--Littlewood maximal function with respect to Euclidean balls with dimensional dependence $O(\sqrt{n} \log n)$. This improves the order of growth in the classical $O(n)$ estimate of Stein and Str\"omberg. The proof goes through a pointwise bound of the Hardy--...

Daniel Spector, Cody B. Stockdale · 0 citations

Preprint Sep 2026

Sharp weighted weak-type bounds for commutators of singular integrals

We establish sharp weak-type bounds for commutators of Calder\'on--Zygmund operators and $\text{BMO}(\mathbb{R}^n)$ symbols with respect to $A_p$ weights. We prove that the bound \looseness=-1 $$ \|[b,T]\|_{L^p(w)\rightarrow L^{p,\infty}(w)}\lesssim [w]_{A_p}^{\max(2,p')} $$ for $p \in (1,\infty)$ and $w \in A_p$ is sh...

A. Mair, Oscar Andres Higuera Ramirez, Cody B. Stockdale · 0 citations