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We provide weighted weak type estimates for square functions, indicating broader implications in analysis.
We provide quantitative weighted weak type estimates for non-integral square functions in the critical case $p=2$ in terms of the Aₚ and reverse Hölder constants associated to the weight. The method of proof uses a decoupling of the role of the weights via a quantitative version of Gehring's lemma. The results can be extended to other p in the range of boundedness of the square function at hand.
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Mena et al. (2025) studied this question.
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