Geodesic
Estimates of Oscillatory Integrals with a Damping Factor
Matematičeskie zametki, Tome 104 (2018) no. 2, pp. 200-215.

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Estimates of the Fourier transform of measures concentrated on analytic hypersurfaces containing a damping factor are considered. The solution of the Sogge and Stein problem on the optimal decrease of the Fourier transform of measures with a damping factor for the particular class of analytic surfaces of three-dimensional space is given.
Keywords: oscillatory integral, damping factor, maximal operator.
Mots-clés : Fourier transform 
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I. A. Ikromov; Sh. A. Muranov. Estimates of Oscillatory Integrals with a Damping Factor. Matematičeskie zametki, Tome 104 (2018) no. 2, pp. 200-215. http://geodesic.mathdoc.fr/item/MZM_2018_104_2_a4/

[1] E. M. Stein, “Maximal functions. I. Spherical means”, Proc. Nat. Acad. Sci. U.S.A., 73:7 (1976), 2174–2175 | DOI | MR | Zbl

[2] E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, Princeton, 1993 | MR | Zbl

[3] C. D. Sogge, Fourier Integrals in Classical Analysis, Cambridge Univ. Press, Cambridge, 1993 | MR | Zbl

[4] A. Greenleaf, “Principal curvature and harmonic analysis”, Indiana Univ. Math. J., 30:4 (1982), 519–537 | DOI | MR | Zbl

[5] C. D. Sogge, “Maximal operators associated to hypersurfaces with one nonvanishing principal curvature”, Fourier Analysis and Partial Differential Equations, Stud. Adv. Math., CRC, Boca Raton, FL, 1995, 317–323 | MR | Zbl

[6] A. Iosevich, E. Sawyer, “Maximal operators over convex hypersurfaces”, Adv. Math., 132:1 (1997), 46–119 | DOI | MR | Zbl

[7] I. A. Ikromov, M. Kempe, D. Müller, “Estimates for maximal functions associated to hypersurfaces in $\mathbb R^3$ and related problems of harmonic analysis”, Acta Math., 204:2 (2010), 151–271 | DOI | MR | Zbl

[8] C. D. Sogge, E. M. Stein, “Averages of functions over hypersurfaces in $\mathbb R^n$”, Invent. Math., 82:3 (1985), 543–556 | DOI | MR | Zbl

[9] M. Cowling, S. Disney, G. Mauceri, D. Müller, “Damping oscillatory integrals”, Invent. Math., 101:2 (1990), 237–260 | DOI | MR | Zbl

[10] D. M. Oberlin, “Oscillatory integrals with polynomial phase”, Math. Scand., 69:1 (1991), 45–56 | DOI | MR | Zbl

[11] D. Mcmichael, “Damping oscillatory integrals with polynomial phase”, Math. Scand., 73:2 (1993), 215–228 | DOI | MR | Zbl

[12] A. Erdeii, Asimptoticheskie razlozheniya, Fizmatgiz, M., 1962 | MR | Zbl

[13] M. V. Fedoryuk, Metod perevala, Nauka, M., 1977 | MR | Zbl

[14] I. A. Ikromov, “Dempfirovannye ostsillyatornye integraly i maksimalnye operatory”, Matem. zametki, 78:6 (2005), 833–852 | DOI | MR | Zbl

[15] I. A. Ikromov, M. Kempe, D. Müller, “Damped oscillatory integrals and boundedness of maximal operators associated to mixed homogeneous hypersurfaces”, Duke Math. J., 126:3 (2005), 471–490 | DOI | MR | Zbl

[16] M. Greenblatt, “$L^p$ boundedness of maximal averages over hypersurfaces in $\mathbb R^3$”, Trans. Amer. Math. Soc., 365:4 (2013), 1875–1900 | DOI | MR | Zbl

[17] E. Zimmermann, On $L^p$-Estimates for Maximal Averages over Hypersurfaces Not Satisfying the Transversality Condition, Doctoral Thesis, Kiel, 2014

[18] G. I. Arkhipov, A. Karatsuba, V. N. Chubarikov, “Trigonometricheskie integraly”, Izv. AN SSSR. Ser. matem., 43:5 (1979), 971–1003 | MR | Zbl

[19] J. G. Van der Corput, “Zahlentheoretische Abschätzungen”, Math. Ann., 84 (1921), 53–79 | DOI | MR | Zbl

[20] B. Malgranzh, Idealy differentsiruemykh funktsii, Mir, M., 1968 | MR

[21] C. S. Hertz, “Fourier transforms related to convex sets”, Ann. of Math. (2), 75 (1962), 81–92 | DOI | MR | Zbl