Lipschitz estimates for commutators of singular integral operators associated with the sections

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• 作者：Guangqing Wang ; Jiang Zhou
• 关键词：Hardy spaces ; commutator ; Lipschitz function ; sections
• 刊名：Journal of Inequalities and Applications
• 出版年：2017
• 出版时间：December 2017
• 年：2017
• 卷：2017
• 期：1
• 全文大小：1683KB
• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X
• 卷排序：2017

文摘

Let H be Monge-Ampère singular integral operator, \(b\in Lip_{\mathcal{F}}^{\beta}\), and \(1/q=1/p-\beta\). It is proved that the commutator \([b,H]\) is bounded from \(L^{p}(\mathbb{R}^{n},d\mu)\) to \(L^{q}(\mathbb{R}^{n},d\mu)\) for \(1< p<1/\beta\) and from \(H^{p}_{\mathcal{F}}(\mathbb{R}^{n})\) to \(L^{q}(\mathbb{R}^{n},d\mu)\) for \(1/(1+\beta)< p\leq1\). For the extreme case \(p=1/(1+\beta)\), a weak estimate is given.