Weighted Bound for Commutators

Yong Ding; Xudong Lai

doi:10.1007/s12220-014-9498-x

Weighted Bound for Commutators

Yong Ding^*
, Xudong Lai

^*Corresponding author for this work

Beijing Normal University
Ministry of Education of the People's Republic of China

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

4 Scopus citations

Abstract

Let K be the Calderón–Zygmund convolution kernel on (Formula presented.). Define the commutator associated with K and (Formula presented.) by (Formula presented.).Recently, Grafakos and Honzík [5] proved that (Formula presented.)is of weak type (1,1) for (Formula presented.). In this paper, we show that (Formula presented.) is also weighted weak type (1,1) with the weight (Formula presented.) for (Formula presented.). Moreover, we prove that (Formula presented.) is bounded on weighted (Formula presented.) for all (Formula presented.).

Original language	English
Pages (from-to)	1915-1938
Number of pages	24
Journal	Journal of Geometric Analysis
Volume	25
Issue number	3
DOIs	https://doi.org/10.1007/s12220-014-9498-x
State	Published - 20 Jul 2015
Externally published	Yes

Keywords

Calderón commutator
Weak type (1, 1)
Weighted

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10.1007/s12220-014-9498-x

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title = "Weighted Bound for Commutators",

abstract = "Let K be the Calder{\'o}n–Zygmund convolution kernel on (Formula presented.). Define the commutator associated with K and (Formula presented.) by (Formula presented.).Recently, Grafakos and Honz{\'i}k [5] proved that (Formula presented.)is of weak type (1,1) for (Formula presented.). In this paper, we show that (Formula presented.) is also weighted weak type (1,1) with the weight (Formula presented.) for (Formula presented.). Moreover, we prove that (Formula presented.) is bounded on weighted (Formula presented.) for all (Formula presented.).",

keywords = "Calder{\'o}n commutator, Weak type (1, 1), Weighted",

author = "Yong Ding and Xudong Lai",

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year = "2015",

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T1 - Weighted Bound for Commutators

AU - Ding, Yong

AU - Lai, Xudong

PY - 2015/7/20

Y1 - 2015/7/20

N2 - Let K be the Calderón–Zygmund convolution kernel on (Formula presented.). Define the commutator associated with K and (Formula presented.) by (Formula presented.).Recently, Grafakos and Honzík [5] proved that (Formula presented.)is of weak type (1,1) for (Formula presented.). In this paper, we show that (Formula presented.) is also weighted weak type (1,1) with the weight (Formula presented.) for (Formula presented.). Moreover, we prove that (Formula presented.) is bounded on weighted (Formula presented.) for all (Formula presented.).

AB - Let K be the Calderón–Zygmund convolution kernel on (Formula presented.). Define the commutator associated with K and (Formula presented.) by (Formula presented.).Recently, Grafakos and Honzík [5] proved that (Formula presented.)is of weak type (1,1) for (Formula presented.). In this paper, we show that (Formula presented.) is also weighted weak type (1,1) with the weight (Formula presented.) for (Formula presented.). Moreover, we prove that (Formula presented.) is bounded on weighted (Formula presented.) for all (Formula presented.).

KW - Calderón commutator

KW - Weak type (1, 1)

KW - Weighted

UR - https://www.scopus.com/pages/publications/84931571826

U2 - 10.1007/s12220-014-9498-x

DO - 10.1007/s12220-014-9498-x

M3 - 文章

AN - SCOPUS:84931571826

SN - 1050-6926

VL - 25

SP - 1915

EP - 1938

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 3

ER -

Weighted Bound for Commutators

Abstract

Keywords

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