Estimates for oscillatory integrals with phase having \(D\) type singularities

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...

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Bibliographic Details
Published in:arXiv.org 2024-02
Main Authors: Akramov, Ibrokhimbek, Ikromov, Isroil A
Format: Article
Language:English
Subjects:
Estimates
Integrals
Singularities
Online Access:Get full text
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Summary: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.
ISSN:2331-8422