In this paper we consider the Sogge- Stein problem related to the damped oscillatory integrals. We show that in three-dimensional Euclidean spaces minimal exponent, which guarantees optimal decaying of the Fourier transform of the surfaces-carried measures with mitigating factor is bounded by 3/2. A proof of the main theorem is based on Weierstrass type results.
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Sadullaev, Azimbay; Ikromov, Isroil; and Muranov, Shaxriddin
"Damped oscillatory integrals and Weierstrass polynomials,"
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 3:
2, Article 15.