Weighted endpoint estimates for singular integral operators associated with zygmund dilations

Yongsheng Han; Ji Li; Chin-Cheng Lin; Chaoqiang Tan; Xinfeng Wu

doi:10.11650/tjm/181203

Weighted endpoint estimates for singular integral operators associated with zygmund dilations

Yongsheng Han, Ji Li, Chin-Cheng Lin^*, Chaoqiang Tan, Xinfeng Wu

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

The main purpose of this paper is to study multi-parameter singular integral operators which commute with Zygmund dilations. We develop the theory of the weighted multi-parameter Hardy space H _z,w ^p and prove the boundedness for these operators on H _z,w ^p for certain p ≤ 1, which provide endpoint estimates for those singular integral operators studied by Ricci-Stein [31] and Fefferman-Pipher [15]. We also establish the Calderón-Zygmund decomposition and interpolation theorem in this setting.

Original language	English
Pages (from-to)	375-408
Number of pages	34
Journal	Taiwanese Journal of Mathematics
Volume	23
Issue number	2
DOIs	https://doi.org/10.11650/tjm/181203
Publication status	Published - Apr 2019

Keywords

Calderón-Zygmund decomposition
interpolation
multi-parameter singular integral operators
weighted Hardy spaces
Zygmund dilations

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title = "Weighted endpoint estimates for singular integral operators associated with zygmund dilations",

abstract = " The main purpose of this paper is to study multi-parameter singular integral operators which commute with Zygmund dilations. We develop the theory of the weighted multi-parameter Hardy space H z,w p and prove the boundedness for these operators on H z,w p for certain p ≤ 1, which provide endpoint estimates for those singular integral operators studied by Ricci-Stein [31] and Fefferman-Pipher [15]. We also establish the Calder{\'o}n-Zygmund decomposition and interpolation theorem in this setting. ",

keywords = "Calder{\'o}n-Zygmund decomposition, interpolation, multi-parameter singular integral operators, weighted Hardy spaces, Zygmund dilations",

author = "Yongsheng Han and Ji Li and Chin-Cheng Lin and Chaoqiang Tan and Xinfeng Wu",

year = "2019",

month = apr,

doi = "10.11650/tjm/181203",

language = "English",

volume = "23",

pages = "375--408",

journal = "Taiwanese Journal of Mathematics",

issn = "2224-6851",

publisher = "Mathematical Society of the Rep. of China",

number = "2",

}

TY - JOUR

T1 - Weighted endpoint estimates for singular integral operators associated with zygmund dilations

AU - Han, Yongsheng

AU - Li, Ji

AU - Lin, Chin-Cheng

AU - Tan, Chaoqiang

AU - Wu, Xinfeng

PY - 2019/4

Y1 - 2019/4

N2 - The main purpose of this paper is to study multi-parameter singular integral operators which commute with Zygmund dilations. We develop the theory of the weighted multi-parameter Hardy space H z,w p and prove the boundedness for these operators on H z,w p for certain p ≤ 1, which provide endpoint estimates for those singular integral operators studied by Ricci-Stein [31] and Fefferman-Pipher [15]. We also establish the Calderón-Zygmund decomposition and interpolation theorem in this setting.

AB - The main purpose of this paper is to study multi-parameter singular integral operators which commute with Zygmund dilations. We develop the theory of the weighted multi-parameter Hardy space H z,w p and prove the boundedness for these operators on H z,w p for certain p ≤ 1, which provide endpoint estimates for those singular integral operators studied by Ricci-Stein [31] and Fefferman-Pipher [15]. We also establish the Calderón-Zygmund decomposition and interpolation theorem in this setting.

KW - Calderón-Zygmund decomposition

KW - interpolation

KW - multi-parameter singular integral operators

KW - weighted Hardy spaces

KW - Zygmund dilations

UR - http://www.scopus.com/inward/record.url?scp=85065891512&partnerID=8YFLogxK

U2 - 10.11650/tjm/181203

DO - 10.11650/tjm/181203

M3 - Article

AN - SCOPUS:85065891512

SN - 2224-6851

VL - 23

SP - 375

EP - 408

JO - Taiwanese Journal of Mathematics

JF - Taiwanese Journal of Mathematics

IS - 2

ER -

Weighted endpoint estimates for singular integral operators associated with zygmund dilations

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Keywords

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