Mathematische Annalen

, Volume 352, Issue 2, pp 293–337 | Cite as

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

Article

Abstract

We establish sharp L2-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 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Raluca Felea
    • 1
  • Allan Greenleaf
    • 2
  • Malabika Pramanik
    • 3
  1. 1.School of of Mathematical SciencesRochester Institute of TechnologyRochesterUSA
  2. 2.Department of MathematicsUniversity of RochesterRochesterUSA
  3. 3.Department of MathematicsUniversity of British ColumbiaVancouverCanada

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