Article

Weierstrass Polynomials in Estimates of Oscillatory Integrals

Isroil A. IkromovSamarkand State University named after A. NavoiAzimbay SadullaevSamarkand State University named after A. Navoi

Contemporary Mathematics Fundamental Directionsjournal2021en

ABI

Abstract

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.

Topics

Advanced Harmonic Analysis Research Advanced Mathematical Modeling in Engineering Advanced Banach Space Theory

Identifiers

DOI: 10.22363/2413-3639-2021-67-4-668-692

Citations and references

Cited by 09 references

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