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15 April 2002 Oscillatory integral operators with low-order degeneracies
Allan Greenleaf, Andreas Seeger
Duke Math. J. 112(3): 397-420 (15 April 2002). DOI: 10.1215/S0012-9074-02-11231-9

Abstract

We prove sharp $L\sp 2$-estimates for oscillatory integral and Fourier integral operators for which the associated canonical relation $\mathscr {C}\subset T\sp \ast\Omega\sb L\times T\sp \ast\Omega\sb R$ projects to $T\sp \ast\Omega\sb L$ and to $T\sp \ast\Omega\sb R$ with corank 1 singularities of type $\leq 2$. This includes two-sided cusp singularities. Applications are given to operators with one-sided swallowtail singularities such as restricted X-ray transforms for well-curved line complexes in five dimensions.

Citation

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Allan Greenleaf. Andreas Seeger. "Oscillatory integral operators with low-order degeneracies." Duke Math. J. 112 (3) 397 - 420, 15 April 2002. https://doi.org/10.1215/S0012-9074-02-11231-9

Information

Published: 15 April 2002
First available in Project Euclid: 18 June 2004

zbMATH: 1033.35164
MathSciNet: MR1896469
Digital Object Identifier: 10.1215/S0012-9074-02-11231-9

Subjects:
Primary: 35S30
Secondary: 42B20 , 47G10 , 58J40

Rights: Copyright © 2002 Duke University Press

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Vol.112 • No. 3 • 15 April 2002
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