The Multilinear Littlewood–Paley Operators with Minimal Regularity Conditions

Mingming Cao; Kôzô Yabuta

doi:10.1007/s00041-018-9613-7

The Multilinear Littlewood–Paley Operators with Minimal Regularity Conditions

Mingming Cao^*
, Kôzô Yabuta

^*Corresponding author for this work

Beijing Normal University
Kwansei Gakuin University

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

16 Scopus citations

Abstract

We investigate the quantitative weighted estimates for a large class of the multilinear Littlewood–Paley square operators. Our kernels satisfy the minimal regularity assumption, called L^r-Hörmander condition. We respectively establish the pointwise sparse domination for the multilinear square functions and their iterated commutators. Based on them, we obtain the strong type quantitative bounds and endpoint estimates. We recover lots of known weighted inequalities for Littlewood–Paley operators. Significantly, the approach is dyadic, quite elementary and simpler than that presented previously.

Original language	English
Pages (from-to)	1203-1247
Number of pages	45
Journal	Journal of Fourier Analysis and Applications
Volume	25
Issue number	3
DOIs	https://doi.org/10.1007/s00041-018-9613-7
State	Published - 15 Jun 2019
Externally published	Yes

Keywords

Littlewood–Paley functions
Multilinear
Quantitative weighted estimates
Sparse operators

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10.1007/s00041-018-9613-7

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title = "The Multilinear Littlewood{\textendash}Paley Operators with Minimal Regularity Conditions",

abstract = "We investigate the quantitative weighted estimates for a large class of the multilinear Littlewood{\textendash}Paley square operators. Our kernels satisfy the minimal regularity assumption, called Lr-H{\"o}rmander condition. We respectively establish the pointwise sparse domination for the multilinear square functions and their iterated commutators. Based on them, we obtain the strong type quantitative bounds and endpoint estimates. We recover lots of known weighted inequalities for Littlewood{\textendash}Paley operators. Significantly, the approach is dyadic, quite elementary and simpler than that presented previously.",

keywords = "Littlewood{\textendash}Paley functions, Multilinear, Quantitative weighted estimates, Sparse operators",

author = "Mingming Cao and K{\^o}z{\^o} Yabuta",

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T1 - The Multilinear Littlewood–Paley Operators with Minimal Regularity Conditions

AU - Cao, Mingming

AU - Yabuta, Kôzô

PY - 2019/6/15

Y1 - 2019/6/15

N2 - We investigate the quantitative weighted estimates for a large class of the multilinear Littlewood–Paley square operators. Our kernels satisfy the minimal regularity assumption, called Lr-Hörmander condition. We respectively establish the pointwise sparse domination for the multilinear square functions and their iterated commutators. Based on them, we obtain the strong type quantitative bounds and endpoint estimates. We recover lots of known weighted inequalities for Littlewood–Paley operators. Significantly, the approach is dyadic, quite elementary and simpler than that presented previously.

AB - We investigate the quantitative weighted estimates for a large class of the multilinear Littlewood–Paley square operators. Our kernels satisfy the minimal regularity assumption, called Lr-Hörmander condition. We respectively establish the pointwise sparse domination for the multilinear square functions and their iterated commutators. Based on them, we obtain the strong type quantitative bounds and endpoint estimates. We recover lots of known weighted inequalities for Littlewood–Paley operators. Significantly, the approach is dyadic, quite elementary and simpler than that presented previously.

KW - Littlewood–Paley functions

KW - Multilinear

KW - Quantitative weighted estimates

KW - Sparse operators

UR - https://www.scopus.com/pages/publications/85045754540

U2 - 10.1007/s00041-018-9613-7

DO - 10.1007/s00041-018-9613-7

M3 - 文章

AN - SCOPUS:85045754540

SN - 1069-5869

VL - 25

SP - 1203

EP - 1247

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

IS - 3

ER -

The Multilinear Littlewood–Paley Operators with Minimal Regularity Conditions

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Keywords

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