Calderón–Zygmund operators on product Hardy spaces
Calderón–Zygmund operators on product Hardy spaces
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DOI：
10.1016/j.jfa.2009.10.022
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发表时间：
2010-04
影响因子：
1.7
通讯作者：
Yongsheng Han;Ming-Yi Lee;Chin-Cheng Lin;Ying-Chieh Lin
中科院分区：
文献类型：
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作者：
Yongsheng Han;Ming-Yi Lee;Chin-Cheng Lin;Ying-Chieh Lin
设T是Jirné引入的乘积Calderón-Zygmund奇异积分。利用Hp(Rn×Rm)的一个优雅的矩形原子分解和Jesné‘S几何覆盖引理，R.Fefferman证明了T的显著的Hp(Rn×Rm)−Lp(Rn×Rm)有界性.本文利用向量值奇异积分、Calderón恒等式、Littlewood-Paley理论和几乎正交性，结合Fefferman的矩形原子分解和Jirné的S覆盖引理，证明了T在乘积HP(Rn×Rm)上有界的充要条件是T1∗(1)=T2∗(1)=0，其中ε是T的核的正则性指数
Let T be a product Calderón–Zygmund singular integral introduced by Journé. Using an elegant rectangle atomic decomposition of Hp(Rn×Rm) and Journé's geometric covering lemma, R. Fefferman proved the remarkable Hp(Rn×Rm)−Lp(Rn×Rm) boundedness of T. In this paper we apply vector-valued singular integral, Calderón's identity, Littlewood–Paley theory and the almost orthogonality together with Fefferman's rectangle atomic decomposition and Journé's covering lemma to show that T is bounded on product Hp(Rn×Rm) for max{nn+ε,mm+ε}<p⩽1 if and only if T1∗(1)=T2∗(1)=0, where ε is the regularity exponent of the kernel of T.