Weighted Weak Type estimates for non-integral Square Functions

2025/06/17 by Mena, Dario, Reguera, Maria Carmen, Roncal, Luz
#42B20 #42B25 (Primary) #42B35 (Secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.14897

Abstract

We provide quantitative weighted weak type estimates for non-integral square functions in the critical case p=2 in terms of the A_p 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.

Citations

• Endpoint weak-type bounds beyond Calderón-Zygmund theory
• Strong weighted and restricted weak weighted estimates of the square function
• Sharp Reverse Hölder property for A_∞ weights on spaces of homogeneous type
• Sharp weighted norm inequalities for Littlewood-Paley operators and\n singular integrals
• The sharp A_p constant for weights in a reverse-Hölder class
• Lectures on the Kato square root problem

Related

• Weighted Weak Type Estimates for Square Functions
• Strong weighted and restricted weak weighted estimates of the square function
• Weak type estimates of intrinsic square functions on the weighted Hardy spaces
• Weighted weak (1,1) estimate for non-commutative square function
• Sharp weak type estimates for weights in the class A_{p1, p2}