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

Daewon Chung; Jean Carlo Moraes; María Cristina Pereyra; Brett D. Wick

doi:10.1007/s12220-025-02221-y

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

Daewon Chung
, Jean Carlo Moraes
, María Cristina Pereyra
, Brett D. Wick

Research output: Contribution to journal › Article › peer-review

Abstract

We present necessary and sufficient conditions on triples of weights (u, v, w) for the boundedness of the dyadic weighted square function Sw 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.

Original language	English
Article number	1
Journal	Journal of Geometric Analysis
Volume	36
Issue number	1
DOIs	https://doi.org/10.1007/s12220-025-02221-y
State	Published - Jan 2026

Keywords

Haar multipliers
dyadic square function
two weight inequalities

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title = "Two-weight estimates for the square function and t-Haar multipliers",

abstract = "We present necessary and sufficient conditions on triples of weights (u, v, w) for the boundedness of the dyadic weighted square function Sw 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.",

keywords = "Haar multipliers, dyadic square function, two weight inequalities",

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AU - Chung, Daewon

AU - Moraes, Jean Carlo

AU - Pereyra, María Cristina

AU - Wick, Brett D.

N1 - Publisher Copyright: © Mathematica Josephina, Inc. 2025.

PY - 2026/1

Y1 - 2026/1

N2 - We present necessary and sufficient conditions on triples of weights (u, v, w) for the boundedness of the dyadic weighted square function Sw 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.

AB - We present necessary and sufficient conditions on triples of weights (u, v, w) for the boundedness of the dyadic weighted square function Sw 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.

KW - Haar multipliers

KW - dyadic square function

KW - two weight inequalities

UR - https://www.scopus.com/pages/publications/105020464654

U2 - 10.1007/s12220-025-02221-y

DO - 10.1007/s12220-025-02221-y

M3 - Article

AN - SCOPUS:105020464654

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VL - 36

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 1

M1 - 1

ER -

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

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Keywords

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