estimates for a singular integral operator motivated by Calder¨®n?s second commutator

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• 作者：Eyvindur Ari Palsson ^{eap48@cornell.edu}
• 关键词：Fourier analysis ; Multilinear operators
• 刊名：Journal of Functional Analysis
• 出版年：2012
• 出版时间：15 February 2012
• 年：2012
• 卷：262
• 期：4
• 页码：1645-1678
• 全文大小：273 K

文摘

We prove a wide range of estimates for a trilinear singular integral operator motivated by dropping one average in Calder¨®n?s second commutator. For comparison by dropping two averages in Calder¨®n?s second commutator one faces the trilinear Hilbert transform. The novelty in this paper is that in order to avoid difficulty of the level of the trilinear Hilbert transform, we choose to view the symbol of the operator as a non-standard symbol. The methods used come from time-frequency analysis but must be adapted to the fact that our symbol is non-standard.