Marcinkiewicz积分算子交换子在Hardy空间及Herz型Hardy空间上的有界性

Acta mathematica scientia,Series A

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Boundedness of the Commutator of Marcinkiewicz Integral on Hardy Space and Herz-type Hardy Space

Cheng Meifang;Shu Lisheng

Department of Mathematics, Nankai University, Tianjin 300071;

Department of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000

Received:2005-02-21 Revised:2007-07-17 Online:2008-04-25 Published:2008-04-25
Contact: Cheng Meifang

Abstract

Abstract: Let $\mu_{\Omega,b}$ be the commutator of the function $b\in$ Lip$_{\beta}(R^{n})$ and the Marcinkiewicz integral operator $\mu_{\Omega}$. In this paper, the authors study the boundedness properties of $\mu_{\Omega,b}$ on the classical Hardy spaces and the Herz-type Hardy spaces.

Key words: Marcinkiewicz integral, Commutator, Herz space, Herz-type Hardy space, Atom, Lipschitz space.

CLC Number:

42B25

Cheng Meifang;Shu Lisheng.

Boundedness of the Commutator of Marcinkiewicz Integral on Hardy Space and Herz-type Hardy Space

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Boundedness of the Commutator of Marcinkiewicz Integral on Hardy Space and Herz-type Hardy Space

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