We consider the Fourier integral operators associated to singular canonical relations, with the cusp singularities on both sides. We prove that such operators lose 1/4+ 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.
Integral operators with two-sided cusp singularities / Andrew, Comech; Cuccagna, Scipio. - In: INTERNATIONAL MATHEMATICS RESEARCH NOTICES. - ISSN 1073-7928. - STAMPA. - 2000:23(2000), pp. 1225-1242. [10.1155/S1073792800000611]
Integral operators with two-sided cusp singularities
CUCCAGNA, Scipio
2000
Abstract
We consider the Fourier integral operators associated to singular canonical relations, with the cusp singularities on both sides. We prove that such operators lose 1/4+ 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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