Open AccessWeierstrass Polynomials in Estimates of Oscillatory Integrals
Author(s) -
Isroil A. Ikromov,
Azimbay Sadullaev
Publication year - 2021
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2021-67-4-668-692
Subject(s) - mathematics , class (philosophy) , fourier transform , function (biology) , mathematical analysis , pure mathematics , computer science , evolutionary biology , artificial intelligence , biology
In this paper, estimates are obtained for the Fourier transform of smooth charges (measures) concentrated on some nonconvex hypersurfaces. The summability of the maximal Randall function is proved for a wide class of nonconvex hypersurfaces. In addition, in the three-dimensional case, estimates are obtained depending on the Varchenko height. The accuracy of the obtained estimates is proved. The proof of the estimate for oscillatory integrals is based on the Weierstrass preparatory theorem.