Estimates for oscillatory integrals with phase having D type singularities

2024/02/06 by Ibrokhimbek Akramov, Akramov, Ibrokhimbek, Isroil A. Ikromov +1
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2402.04167

openalex publication_date 2024/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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