Calderón–Zygmund operators on product Hardy spaces

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• 作者：Yongsheng Han ; Ming-Yi Lee ; Chin-Cheng Lin ; Ying-Chieh Lin
• 关键词：Calderó ; n– ; Zygmund operators ; Journé ; 's class ; Littlewood– ; Paley function ; Product Hardy spaces
• 刊名：Journal of Functional Analysis
• 出版年：2010
• 出版时间：15 April 2010
• 年：2010
• 卷：258
• 期：8
• 页码：2834-2861
• 全文大小：299 K

文摘

Let T be a product Calderón–Zygmund singular integral introduced by Journé. Using an elegant rectangle atomic decomposition of and Journé's geometric covering lemma, R. Fefferman proved the remarkable 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 for if and only if , where ε is the regularity exponent of the kernel of T.