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• W1506421908 abstract "In this paper we give examples of polynomial phase functions for which the factorization condition of Seeger, Sogge and Stein (Ann. Math. <bold>134</bold> (1991)) fails. The corresponding Fourier integral operators turn out to be still continuous in <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L Superscript p> <mml:semantics> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <mml:annotation encoding=application/x-tex>L^p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We also give examples of the failure of the factorization condition for translation invariant operators. In this setting the frequency space must be at least 5-dimensional, which shows that the examples are optimal. We briefly discuss the stationary phase method for the corresponding operators." @default.
• W1506421908 created "2016-06-24" @default.
• W1506421908 creator A5014446077 @default.
• W1506421908 date "2001-10-12" @default.
• W1506421908 modified "2023-09-26" @default.
• W1506421908 title "On the failure of the factorization condition for non-degenerate Fourier integral operators" @default.
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• W1506421908 doi "https://doi.org/10.1090/s0002-9939-01-06210-4" @default.
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