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International Mathematics Research Notices (2000) 2000:1225-1242, doi:10.1155/S1073792800000611
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Copyright © 2000 Hindawi Publishing Corporation. All rights reserved.

Integral operators with two-sided cusp singularities

Andrew Comech and Scipio Cuccagna

We consider the Fourier integral operators associated to singular canonical relations, with the cusp singularities on both sides. We prove that such operators lose Formula of a derivative in smoothing properties, compared to nonsingular Fourier integral operators. We also state the results on regularity properties in Lp spaces. Our approach is based on almost orthogonality decompositions of singular oscillatory integral operators.


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