PreprintCC BY 4.0arXiv
On the weighted weak-type constant for the dyadic square function
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]A2.
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BibTeX
@misc{osekowski2026weighted,
title = {{On the weighted weak-type constant for the dyadic square function}},
author = {Adam Osekowski},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14430},
eprint = {2609.14430},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14430},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the weighted weak-type constant for the dyadic square function
AU - Adam Osekowski
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14430
UR - https://arxiv.org/abs/2609.14430
AB - 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.
ER -