Mathematische Annalen

, Volume 352, Issue 2, pp 293-337

First online:

An FIO calculus for marine seismic imaging, II: Sobolev estimates

  • Raluca FeleaAffiliated withSchool of of Mathematical Sciences, Rochester Institute of Technology
  • , Allan GreenleafAffiliated withDepartment of Mathematics, University of Rochester Email author 
  • , Malabika PramanikAffiliated withDepartment of Mathematics, University of British Columbia

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We establish sharp L 2-Sobolev estimates for classes of pseudodifferential operators with singular symbols [Guillemin and Uhlmann (Duke Math J 48:251–267, 1981), Melrose and Uhlmann (Commun Pure Appl Math 32:483–519, 1979)] whose non-pseudodifferential (Fourier integral operator) parts exhibit two-sided fold singularities. The operators considered include both singular integral operators along curves in \({\mathbb R^2}\) with simple inflection points and normal operators arising in linearized seismic imaging in the presence of fold caustics [Felea (Comm PDE 30:1717–1740, 2005), Felea and Greenleaf (Comm PDE 33:45–77, 2008), Nolan (SIAM J Appl Math 61:659–672, 2000)].

Mathematics Subject Classification (2000)

35S05 35S30