Geodesic
Weierstrass polynomials in estimates of oscillatory integrals
Contemporary Mathematics. Fundamental Directions, Science — Technology — Education — Mathematics — Medicine, Tome 67 (2021) no. 4, pp. 668-692

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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. 
@article{CMFD_2021_67_4_a4,
     author = {I. A. Ikromov and A. S. Sadullaev},
     title = {Weierstrass polynomials in estimates of oscillatory integrals},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {668--692},
     publisher = {mathdoc},
     volume = {67},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2021_67_4_a4/}
}
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I. A. Ikromov; A. S. Sadullaev. Weierstrass polynomials in estimates of oscillatory integrals. Contemporary Mathematics. Fundamental Directions, Science — Technology — Education — Mathematics — Medicine, Tome 67 (2021) no. 4, pp. 668-692. http://geodesic.mathdoc.fr/item/CMFD_2021_67_4_a4/