Weak and strong type estimates for the multilinear pseudo-differential operators

Mingming Cao; Qingying Xue; Kôzô Yabuta

doi:10.1016/j.jfa.2019.108454

Weak and strong type estimates for the multilinear pseudo-differential operators

Mingming Cao^*
, Qingying Xue
, Kôzô Yabuta

^*Corresponding author for this work

Sun Yat-Sen University
CSIC
Beijing Normal University
Kwansei Gakuin University

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

20 Scopus citations

Abstract

In this paper, we investigate the boundedness of the multilinear pseudo-differential operator T_σ. First, we establish the local exponential decay estimates for T_σ. In terms of the corresponding commutators T_σ,Σb, we obtain the local subexponential decay estimates. Secondly, we derive the weighted mixed weak type inequality for T_σ, which parallels Sawyer's conjecture for Calderón-Zygmund operators and covers the endpoint weighted inequalities. Last but not least, we present the sharp weighted estimates for T_σ and T_σ,Σb. It is worth mentioning that our results are totally new even in the linear case.

Original language	English
Article number	108454
Journal	Journal of Functional Analysis
Volume	278
Issue number	10
DOIs	https://doi.org/10.1016/j.jfa.2019.108454
State	Published - 1 Jun 2020
Externally published	Yes

Keywords

Endpoint weak bounds
Local decay estimates
Pseudo-differential operators
Sharp weighted inequalities

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10.1016/j.jfa.2019.108454

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title = "Weak and strong type estimates for the multilinear pseudo-differential operators",

abstract = "In this paper, we investigate the boundedness of the multilinear pseudo-differential operator Tσ. First, we establish the local exponential decay estimates for Tσ. In terms of the corresponding commutators Tσ,Σb, we obtain the local subexponential decay estimates. Secondly, we derive the weighted mixed weak type inequality for Tσ, which parallels Sawyer's conjecture for Calder{\'o}n-Zygmund operators and covers the endpoint weighted inequalities. Last but not least, we present the sharp weighted estimates for Tσ and Tσ,Σb. It is worth mentioning that our results are totally new even in the linear case.",

keywords = "Endpoint weak bounds, Local decay estimates, Pseudo-differential operators, Sharp weighted inequalities",

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

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year = "2020",

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doi = "10.1016/j.jfa.2019.108454",

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T1 - Weak and strong type estimates for the multilinear pseudo-differential operators

AU - Cao, Mingming

AU - Xue, Qingying

AU - Yabuta, Kôzô

PY - 2020/6/1

Y1 - 2020/6/1

N2 - In this paper, we investigate the boundedness of the multilinear pseudo-differential operator Tσ. First, we establish the local exponential decay estimates for Tσ. In terms of the corresponding commutators Tσ,Σb, we obtain the local subexponential decay estimates. Secondly, we derive the weighted mixed weak type inequality for Tσ, which parallels Sawyer's conjecture for Calderón-Zygmund operators and covers the endpoint weighted inequalities. Last but not least, we present the sharp weighted estimates for Tσ and Tσ,Σb. It is worth mentioning that our results are totally new even in the linear case.

AB - In this paper, we investigate the boundedness of the multilinear pseudo-differential operator Tσ. First, we establish the local exponential decay estimates for Tσ. In terms of the corresponding commutators Tσ,Σb, we obtain the local subexponential decay estimates. Secondly, we derive the weighted mixed weak type inequality for Tσ, which parallels Sawyer's conjecture for Calderón-Zygmund operators and covers the endpoint weighted inequalities. Last but not least, we present the sharp weighted estimates for Tσ and Tσ,Σb. It is worth mentioning that our results are totally new even in the linear case.

KW - Endpoint weak bounds

KW - Local decay estimates

KW - Pseudo-differential operators

KW - Sharp weighted inequalities

UR - https://www.scopus.com/pages/publications/85077364399

U2 - 10.1016/j.jfa.2019.108454

DO - 10.1016/j.jfa.2019.108454

M3 - 文章

AN - SCOPUS:85077364399

SN - 0022-1236

VL - 278

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 10

M1 - 108454

ER -

Weak and strong type estimates for the multilinear pseudo-differential operators

Abstract

Keywords

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