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Scientific Journal of Samarkand University

Abstract

In this paper we consider estimates of the Fourier transform measures, concentrated on analytic hypersurfaces containing the of damping factor. The paper presents the solution of the problem S.D.Soggi and I.M. Stein about the optimal decay of the transformation Fourier measures with a damping factor for any analytic surfaces in three-dimensional Euclidean space.

First Page

3

Last Page

10

References

1. C. D. Sogge, E. M. Stein. Averages of functions over hypersurfaces in Invent. Math 82543-5561985. 2. D. M. Oberlin. Oscillatory integrals with polynomial phase. MATH.SCAND 69, 45-56, 1991. 3. I.A.Ikromov, Sh.A.Muranov. Ob otsenkax ossilyatirnix integralov c mnojetelem gasheniya Matematicheskiya zametki.104, 2, s. 236-251, 2018. 4. Sh.A.Muranov. On estimates for oscillatory integrals with damping factor. Uzbek Mathematical Journal, 4, 112-125, 2018. 5. Arkhipov G.I., Karatsuba A.A. and Chubarikov V.N.. Trigonometric integrals. Izv. Akad. Nauk SSSR Ser. Mat. 43(5), 971-1003 1197 (Russian); English translation in Math. USSR-Izv., 15(1980),pp 21-239. 6. A.S. Sadullayev. Kriteriy algebraichnosti analiticheskix mnojestv. Funk. Analiz I ego pril. 6, s.85-86, 1972. 7. I.A.Ikromov. Dempfirovannie ossillyatorniy integraly i maksimal’nie operatory. Matematicheskiya zametki, 78,s. 833-852, 2005. 8. A. Erdeyn. Asimptoticheskiye razlojeniya M. Fizmatgiz 1962 9. M.V. Fedoryuk. Metod perevala. Nauka. M. 1977. 10. I. A. Ikromov, D. Müller, M. Kempe. Dampedoscillatoryintegralsandboundedness of maximal operators associated to mixed homogeneous hypersurfaces. DukeMath.J. 126 no.3, р.471-490. 2005.

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