带有加权Lipschitz函数的交换子的有界性

Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (1): 152-164.

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The Boundedness of Commutators with the Weighted Lipschitz Functions

KONG Xiang-Bo, JIANG Yin-Sheng**, ZHANG Lin

1.The Middle School Attached to Xinjiang University, Urumqi 830046;
2.College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046;
3.Department of Applied Mathematics, Xinjiang Institue of Finance and Economics, Urumqi 830012

Received:2010-12-15 Revised:2012-10-22 Online:2013-02-25 Published:2013-02-25
Contact: JIANG Yin-Sheng，ysjiang@xju,edu.cn E-mail:kxbqf@yahoo.com.cn; ysjiang@xju,edu.cn; zhanglin8113@yahoo.com.cn
Supported by:
国家自然科学基金 (10861010, 11161044)资助

Abstract

Abstract:

Let T_b be commutator of the weighted Lipschitz function b and the Calder'{o}n-Zygmund singular integral operator T. In this paper, we study the boundedness properties of T_b on some weighted spaces: weighted Hardy space, weighted Herz spaces and weighted Herz-type Hardy
spaces. In addition, we also obtain its corresponding endpoint estimates.

Key words: Singular integral, Commutator, Weighted Hardy space, Weighted Herz spaces, Weighted Herz-type Hardy spaces

CLC Number:

42B20

KONG Xiang-Bo, JIANG Yin-Sheng, ZHANG Lin. The Boundedness of Commutators with the Weighted Lipschitz Functions[J].Acta mathematica scientia,Series A, 2013, 33(1): 152-164.

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The Boundedness of Commutators with the Weighted Lipschitz Functions

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