Estimating Oscillatory Integrals of Convolution Type in $\mathbb{R}^d$

Aleksandra Niepla; Kevin O'Neill; Zhen Zeng

Estimating Oscillatory Integrals of Convolution Type in $\mathbb{R}^d$

Classical Analysis and ODEs 2021-07-23 v2

Authors: Aleksandra Niepla , Kevin O'Neill , Zhen Zeng

Abstract

In this paper, we prove an $L^2-L^2-L^2$ decay estimate for a trilinear oscillatory integral of convolution type in $\mathbb{R}^d,$ which recovers the earlier result of Li (2013) when $d=1.$ We discuss the sharpness of our result in the $d=2$ case. Our main hypothesis has close connections to the property of simple nondegeneracy studied by Christ, Li, Tao and Thiele (2005).

Cite

@article{arxiv.1811.05098,
  title  = {Estimating Oscillatory Integrals of Convolution Type in $\mathbb{R}^d$},
  author = {Aleksandra Niepla and Kevin O'Neill and Zhen Zeng},
  journal= {arXiv preprint arXiv:1811.05098},
  year   = {2021}
}

Comments

Application of Theorem 2.1 in the proof of Theorem 1.2 assumed uniformity of the constant C which does not hold in general; in reality, there may be dependence on the phase

Estimating Oscillatory Integrals of Convolution Type in $\mathbb{R}^d$

Abstract

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