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This is a Quantitative Study study.

October 20, 2025Open Access

Weighted Weak Type estimates for non-integral Square Functions

Puntos clave

Weighted weak type estimates yield insights for non-integral square functions in critical case $p=2$.
Findings are expressed in terms of $A_p$ and reverse Hölder constants associated with the weight.
Decoupling the role of weights is achieved using a quantitative version of Gehring's lemma.
Results extend to other $p$ values within the boundedness range of related square functions.

Resumen

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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