Archiv der Mathematik

, Volume 72, Issue 1, pp 68–76 | Cite as

Analytic Fourier integral operators, Monge-Ampère equation and holomorphic factorization

  • Michael Ruzhansky


We will show that the factorization condition for the Fourier integral operators \(I_\rho ^\mu (X,Y;\it\Lambda )\) leads to a parametrized parabolic Monge-Ampère equation. For an analytic operator, the fibration by the kernels of the Hessian of phase function is shown to be analytic in a number of cases, by considering a more general continuation problem for the level sets of a holomorphic mapping. The results are applied to obtain L p -continuity for translation invariant operators in \({\Bbb R}^n\) with \(n\leq 4\) and for arbitrary \({\Bbb R}^n\) with \(d\pi _{X\times Y}|_\Lambda \leq n+2\).


Analytic Operator Integral Operator Holomorphic Mapping Factorization Condition Phase Function 
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Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  • Michael Ruzhansky
    • 1
  1. 1.Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USAUS

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