Two-weight estimates for the square function and t-Haar multipliers

2025/01/27 by Chung, Daewon, Moraes, Jean Carlo, Pereyra, María Cristina +1
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.16272

Abstract

We present necessary and sufficient conditions on triples of weights (u,v,w) for the boundedness of the dyadic weighted square function S_w from L²(u) into L²(v). We use this characterization to obtain necessary and sufficient conditions for the boundedness of the t-Haar multipliers from L²(u) into L²(v) in terms of boundedness of the dyadic weighted square function.

Related

• Weighted Inequalities for t-Haar multipliers
• Multilinear dyadic operators and their commutators in the weighted setting
• Bellman functions and two weight inequalities for Haar multipliers
• On two weight estimates for dyadic operators
• A note on a two-weight estimate for the dyadic square function