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arXiv · 2609.14430

On the weighted weak-type constant for the dyadic square function

Adam Osekowski
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Abstract

We present an explicit construction of examples showing that the estimate $ \|S(f)\|_{L^2(w)\to L^{2,\infty}(w)}\lesssim \big([w]_{A_2} \log(1 + [w]_{A_2})\big)^{1/2}$ for the dyadic square function is sharp in terms of the characteristic $[w]_{A_2}$.

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Adam Osekowski. 2026-09-13. On the weighted weak-type constant for the dyadic square function. https://arxiv.org/abs/2609.14430

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