Weighted weak type (1, 1) estimate for the Christ-Journé type commutator

Yong Ding; Xudong Lai

doi:10.1007/s11425-016-9025-x

Weighted weak type (1, 1) estimate for the Christ-Journé type commutator

Yong Ding
, Xudong Lai^*

^*Corresponding author for this work

School of Mathematics

Beijing Normal University

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

2 Scopus citations

Abstract

Let K be the Calderón-Zygmund convolution kernel on R^d (d ≥ 2). Christ and Journé de0ned the commutator associated with K and a ∈ L1^∞(ℝ^d) by (Formula presented.) which is an extension of the classical Calderón commutator. In this paper, we show that T_a is weighted weak type (1, 1) bounded with A₁ weight for d ≥ 2.

Original language	English
Pages (from-to)	517-534
Number of pages	18
Journal	Science China Mathematics
Volume	61
Issue number	3
DOIs	https://doi.org/10.1007/s11425-016-9025-x
State	Published - 1 Mar 2018

Keywords

A weight
Christ-Journé type commutator
weighted weak type (1, 1)

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title = "Weighted weak type (1, 1) estimate for the Christ-Journ{\'e} type commutator",

abstract = "Let K be the Calder{\'o}n-Zygmund convolution kernel on Rd (d ≥ 2). Christ and Journ{\'e} de0ned the commutator associated with K and a ∈ L1∞(ℝd) by (Formula presented.) which is an extension of the classical Calder{\'o}n commutator. In this paper, we show that Ta is weighted weak type (1, 1) bounded with A1 weight for d ≥ 2.",

keywords = "A weight, Christ-Journ{\'e} type commutator, weighted weak type (1, 1)",

author = "Yong Ding and Xudong Lai",

note = "Publisher Copyright: {\textcopyright} 2017, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.",

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doi = "10.1007/s11425-016-9025-x",

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T1 - Weighted weak type (1, 1) estimate for the Christ-Journé type commutator

AU - Ding, Yong

AU - Lai, Xudong

PY - 2018/3/1

Y1 - 2018/3/1

N2 - Let K be the Calderón-Zygmund convolution kernel on Rd (d ≥ 2). Christ and Journé de0ned the commutator associated with K and a ∈ L1∞(ℝd) by (Formula presented.) which is an extension of the classical Calderón commutator. In this paper, we show that Ta is weighted weak type (1, 1) bounded with A1 weight for d ≥ 2.

AB - Let K be the Calderón-Zygmund convolution kernel on Rd (d ≥ 2). Christ and Journé de0ned the commutator associated with K and a ∈ L1∞(ℝd) by (Formula presented.) which is an extension of the classical Calderón commutator. In this paper, we show that Ta is weighted weak type (1, 1) bounded with A1 weight for d ≥ 2.

KW - A weight

KW - Christ-Journé type commutator

KW - weighted weak type (1, 1)

UR - https://www.scopus.com/pages/publications/85035081406

U2 - 10.1007/s11425-016-9025-x

DO - 10.1007/s11425-016-9025-x

M3 - 文章

AN - SCOPUS:85035081406

SN - 1674-7283

VL - 61

SP - 517

EP - 534

JO - Science China Mathematics

JF - Science China Mathematics

IS - 3

ER -

Weighted weak type (1, 1) estimate for the Christ-Journé type commutator

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Keywords

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