The Journal of Geometric Analysis

, Volume 15, Issue 3, pp 405–423 | Cite as

Estimates on level set integral operators in dimension two

  • A. ComechEmail author
  • S. Roudenko


Both oscillatory integral operators and level set operators appear naturally in the study of properties of degenerate Fourier integral operators (such as generalized Randon transforms). The properties of oscillatory integral operators have a longer history and are better understood. On the other hand, level set operators, while sharing many common characteristics with oscillatory integral operators, are easier to handle.

We study L2-estimates on level set operators in dimension two and compare them with what is known about oscillatory integral operators. The cases include operators with non-degenerate phase functions and the level set version of Melrose-Taylor transform (as an example of a degenerate phase function). The estimates are formulated in terms of the Newton polyhedra and type conditions.

Math Subject Classifications

42B25 42B10 

Key Words and Phrases

Fourier integral operators degenerate phase function level set integral operators Melrose-Taylor transform 


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© Mathematica Josephina, Inc. 2005

Authors and Affiliations

  1. 1.Texas A&M UniversityUSA
  2. 2.Duke UniversityDurhamUSA

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