Quantitative weighted estimates for the Littlewood-Paley square function and Marcinkiewicz multipliers

Andrei K. Lerner

doi:https://doi.org/10.4310/MRL.2019.v26.n2.a7

Quantitative weighted estimates for the Littlewood-Paley square function and Marcinkiewicz multipliers

Andrei K. Lerner

Department of Mathematics

Bar-Ilan University

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

Abstract

Quantitative weighted estimates are obtained for the Littlewood-Paley square function S associated with a lacunary decomposition of R and for the Marcinkiewicz multiplier operator. In particular, we find the sharp dependence on [w]_Ap for the L^p(w) operator norm of S for 1 < p ≤ 2.

Original language	English
Pages (from-to)	537-556
Number of pages	20
Journal	Mathematical Research Letters
Volume	26
Issue number	2
DOIs	https://doi.org/10.4310/MRL.2019.v26.n2.a7
State	Published - 2019

All Science Journal Classification (ASJC) codes

General Mathematics

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title = "Quantitative weighted estimates for the Littlewood-Paley square function and Marcinkiewicz multipliers",

abstract = "Quantitative weighted estimates are obtained for the Littlewood-Paley square function S associated with a lacunary decomposition of R and for the Marcinkiewicz multiplier operator. In particular, we find the sharp dependence on [w]Ap for the Lp(w) operator norm of S for 1 < p ≤ 2.",

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year = "2019",

doi = "https://doi.org/10.4310/MRL.2019.v26.n2.a7",

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T1 - Quantitative weighted estimates for the Littlewood-Paley square function and Marcinkiewicz multipliers

AU - Lerner, Andrei K.

PY - 2019

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N2 - Quantitative weighted estimates are obtained for the Littlewood-Paley square function S associated with a lacunary decomposition of R and for the Marcinkiewicz multiplier operator. In particular, we find the sharp dependence on [w]Ap for the Lp(w) operator norm of S for 1 < p ≤ 2.

AB - Quantitative weighted estimates are obtained for the Littlewood-Paley square function S associated with a lacunary decomposition of R and for the Marcinkiewicz multiplier operator. In particular, we find the sharp dependence on [w]Ap for the Lp(w) operator norm of S for 1 < p ≤ 2.

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U2 - https://doi.org/10.4310/MRL.2019.v26.n2.a7

DO - https://doi.org/10.4310/MRL.2019.v26.n2.a7

M3 - مقالة

SN - 1073-2780

VL - 26

SP - 537

EP - 556

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 2

ER -

Quantitative weighted estimates for the Littlewood-Paley square function and Marcinkiewicz multipliers

Abstract

All Science Journal Classification (ASJC) codes

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