Some new decay estimates for (2+1)-dimensional degenerate oscillatory integral operators

2023/08/10 by Tan, Yuxin, Xu, Shaozhen · 1 citation
#42B20 #47G10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.05631

Abstract

In this paper, we consider the (2+1)-dimensional oscillatory integral operators with cubic homogeneous polynomial phases, which are degenerate in the sense of \citeTan06. We improve the previously known L²→ L² decay rate to 3/8 and also establish a sharp L²→ L⁶ decay estimate based on fractional integration method.

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• Sharp L² decay rate for (1+2)-dimensional oscillatory integral operators with cubic polynomial phases

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