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 [
Citation: Jiawei Shen, Jie Yang. $ L^p $ boundedness of oscillatory singular integrals with nonstandard kernels[J]. AIMS Mathematics, 2026, 11(7): 20254-20266. doi: 10.3934/math.2026822
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 [
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Jiawei Shen, Jie Yang. $ L^p $ boundedness of oscillatory singular integrals with nonstandard kernels[J]. AIMS Mathematics, 2026, 11(7): 20254-20266. doi: 10.3934/math.2026822
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