Variational estimates for the bilinear iterated Fourier integral

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• 作者：Yen Do^a ; ¹ ; ^{yendo@virginia.edu} ; Camil Muscalu^b ; ² ; ^{camil@math.cornell.edu} ; Christoph Thiele^c ; ³ ; ^{thiele@math.uni-bonn.de}
• 关键词：42B20
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：272
• 期：5
• 页码：2176-2233
• 全文大小：843 K
• 卷排序：272

文摘

We prove pointwise variational LpLp bounds for a bilinear Fourier integral operator in a large but not necessarily sharp range of exponents. This result is a joint strengthening of the corresponding bounds for the classical Carleson operator, the bilinear Hilbert transform, the variation norm Carleson operator, and the bi-Carleson operator. Terry Lyon's rough path theory allows for extension of our result to multilinear estimates. We consider our result a proof of concept for a wider array of similar estimates with possible applications to ordinary differential equations.