$ L^p $ boundedness of oscillatory singular integrals with nonstandard kernels
Abstract
In this paper, we study a kind of oscillatory singular integral operator $ T_{P, \Omega, A} $ defined by$ T_{P, \Omega, A}f(x) = \text{p.v.} \int_{\mathbb{R}^n} e^{iP(x-y)}\frac{\Omega(x-y)\left[A(x)-A(y)-\nabla A(y)\cdot(x-y)\right]}{|x-y|^{n+1}} f(y)dy, $where $ P(x) $ is a real polynomial on $ \mathbb{R}^n, $ and $ \Omega(\lambda x) = \Omega(x). $ Under some conditions, we show that $ T_{P, \Omega, A} $ is bounded on $ L^p(\mathbb{R}^{n}) $ with uniform boundedness, which improves and extends Pan's result [11].
Fields of Study & Subjects
Advanced Harmonic Analysis Research
Nonlinear Differential Equations Analysis
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- AIMS Mathematics
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 11
- Issue
- 7
- Pages
- 20254–20266
- Publication date
- 1 January 2026