Uniform estimates for oscillatory integrals with smooth phase
Čebyševskij sbornik, Tome 25 (2024) no. 1, pp. 42-51.

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We consider the problem on uniform estimates for an oscillatory integrals with the smooth phase functions having singularities $D_{\infty} $. The estimate is sharp and analogy to estimates of the work of V. N. Karpushkin.
Keywords: phase, deformation, singularity.
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I. A. Ikromov; A. R. Safarov. Uniform estimates for oscillatory integrals with smooth phase. Čebyševskij sbornik, Tome 25 (2024) no. 1, pp. 42-51. http://geodesic.mathdoc.fr/item/CHEB_2024_25_1_a3/

[1] Arnold, V.I., Gusein-Zade, S.M., Varchenko, A., Singularities of Differentiable Maps, Birkhauser, Boston–Basel–Stuttgart, 1985 | MR | Zbl

[2] Varchenko, A., “Newton polyhedra and estimation of oscillating integrals”, Functional Analysis and Its Applications, 10 (1976), 175–196 | DOI | MR

[3] Vladimirov, V.S., Mathematic physics equation, Nauka, M., 1981 (Russian) | MR

[4] Van der Korput K.G., “Zur Methode der stationaren phase”, Compositio Math., 1 (1934), 15–38 | MR | Zbl

[5] Duistermaat J., “Oscillatory integrals Lagrange immersions and unifoldings of singularities”, Comm. Pure. Appl. Math., 27:2 (1974), 207–281 | DOI | MR | Zbl

[6] Ikromov I.A., Muller D., “On adapted coordinate systems”, Trans. Amer. Math. Soc., 363:6 (2011), 2821–2848 | DOI | MR | Zbl

[7] Karpushkin, V., “Uniform estimates for oscillatory integrals with parabolic or hyperbolic phase”, Proceedings of the I.G. Petrovsky Seminar, 9, 1983, 3–39 (Russian) | MR | Zbl

[8] Sogge C.D., Fourier integrals in Classical Analysis, Cambridge university press, Cambridge, 1993, 105 pp. | MR | Zbl

[9] Carbery A., Christ M., and Wright J., “Multidimensional Van der Korput lemma and sublevel set estimates”, Journal of AMS, 12 (1999), 981–1015 | MR | Zbl

[10] Ruzhansky M., Safarov A. R., Khasanov G. A., “Uniform estimates for oscillatory integrals with homogeneous polynomial phases of degree 4”, Analysis and Mathematical Physics, 12(130) (2022) | DOI | MR | Zbl

[11] Safarov, A., “Invariant estimates for double oscillatory integrals”, Mathematical Notes, 104:2 (2018), 293–302 | DOI | DOI | MR | Zbl

[12] Safarov A., “On the $L^p$-bound for trigonometric integrals”, Analysis mathematica, 45 (2019), 153–176 | DOI | MR | Zbl

[13] Safarov A., “On invariant estimates for oscillatory integrals with polynomial phase”, J. Sib. Fed. Univ. Math. Phys., 9 (2016), 102–107 | DOI | MR | Zbl

[14] Safarov A., “On a problem of restriction of Fourier transform on a hypersurface”, Russian Mathematics, 63:4 (2019), 57–63 | DOI | MR | Zbl

[15] Safarov A. R., “Estimates for Mittag–Leffler Functions with Smooth Phase Depending on Two Variables”, J. Sib. Fed. Univ. Math. Phys., 15:4 (2022), 459–466 | MR