Estimates for rough Fourier integral and pseudodifferential operators and applications to the boundedness of multilinear operators

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• 作者：Salvador Rodrí ; guez-Ló ; pez ; ^{salvador@math.uu.se} ; Wolfgang Staubach ^{wulf@math.uu.se}
• 关键词：Fourier integral operators ; Pseudodifferential operators ; Multilinear operators
• 刊名：Journal of Functional Analysis
• 出版年：2013
• 出版时间：15 May, 2013
• 年：2013
• 卷：264
• 期：10
• 页码：2356-2385
• 全文大小：298 K

文摘

We study the boundedness of rough Fourier integral and pseudodifferential operators, defined by general rough H?rmander class amplitudes, on Banach and quasi-Banach spaces. Thereafter we apply the aforementioned boundedness in order to improve on some of the existing boundedness results for H?rmander class bilinear pseudodifferential operators and certain classes of bilinear (as well as multilinear) Fourier integral operators. For these classes of amplitudes, the boundedness of the aforementioned Fourier integral operators turn out to be sharp. Furthermore we also obtain results for rough multilinear operators.