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arXiv · 2402.04167

Estimates for oscillatory integrals with phase having $D$ type singularities

Ibrokhimbek Akramov·Isroil A. Ikromov
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Abstract

In this paper, we consider estimates for the two-dimensional oscillatory integrals. The phase function of the oscillatory integrals is the linear perturbation of a function having $D$ type singularities. We consider estimates for the oscillatory integrals in terms of the Randol's type maximal functions. We obtain a sharp $L^p_{loc}$ estimates for the Randol's maximal functions. Moreover, we investigate the sharp exponent $p$ depending on whether, the phase function has linearly adapted coordinates system or not.

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Ibrokhimbek Akramov, Isroil A. Ikromov. 2024-02-06. Estimates for oscillatory integrals with phase having $D$ type singularities. https://arxiv.org/abs/2402.04167

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