Geodesic
$L^p$-bound for the Fourier transform of surface-carried measures supported on hypersurfaces with $D_\infty$ type singularities
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 3, pp. 350-359 Cet article a éte moissonné depuis la source Math-Net.Ru

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Estimate for Fourier transform of surface-carried measures supported on non-convex surfaces of three-dimensional Euclidean space is considered in this paper.The exact convergence exponent was found wherein the Fourier transform of measures is integrable in tree-dimensional space. This result gives an answer to the question posed by Erdösh and Salmhofer.
Keywords: oscillatory integral, surface-carried measure.
Mots-clés : Fourier transform 
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     title = {$L^p$-bound for the {Fourier} transform of surface-carried measures supported on hypersurfaces with $D_\infty$ type singularities},
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Nigina A. Soleeva. $L^p$-bound for the Fourier transform of surface-carried measures supported on hypersurfaces with $D_\infty$ type singularities. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 3, pp. 350-359. http://geodesic.mathdoc.fr/item/JSFU_2020_13_3_a8/

[1] G.I. Arkhipov, A.A. Karatsuba, V.N. Chubarilov, “Tringonometric integrals”, Izv. AN SSSR, Ser. Mat., 43:5 (1979), 971–1003 (in Russian) | MR

[2] L. Erdös, M. Salmhofer, Math. Z., 257 (2007), 261–294 | DOI | MR | Zbl

[3] B. Randol, “On the asymptotic behavior of the Fourier transform of the indicator function of a convex set”, Trans. AMS, 139 (1969), 278–285 | MR

[4] V.I. Arnold, A.N. Varchenko, S.M. Huseyn-zade, Features of differentiable mappings, v. 1, Classification of critical points of caustics and wave fronts, Nauka, M., 1982 (in Russian) | MR

[5] E.M. Stein, Harmonic analysis, Real-valued methods and oscillatory integrals, Princeton University Press, Princeton, 1993 | MR

[6] I.A. Ikromov, D. Müller, Fourier restriction for hypersurfaces in three dimensions and Newton polyhedra, Annals of Mathematics Studies, 194, Princeton–Oxford, 2016 | MR | Zbl

[7] I.A. Ikromov, Functional Anal. and Its Appl., 29:3 (1995), 161–168 | DOI | MR

[8] V.N. Karpushkin, J. Math. Sci., 35 (1986), 2809–2826 | DOI | Zbl