Sharp Bounds for Oscillatory Integral Operators with Homogeneous Polynomial Phases
Sharp Bounds for Oscillatory Integral Operators with Homogeneous Polynomial Phases
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DOI：
10.4153/s000843951900081x
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发表时间：
2019-05
期刊：
影响因子：
--
通讯作者：
Danqing He;Zuoshunhua Shi
中科院分区：
文献类型：
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作者：
Danqing He;Zuoshunhua Shi
摘要我们得到了具有一般齐次多项式相位的多元振荡积分算子的L^{p}$界。本文考虑的阶段满足秩一条件，这是一个重要的概念介绍了Greenleaf，Pramanik和唐。在一定的附加假设下，我们可以建立具有临界指数的尖锐阻尼估计来证明端点L^{p}估计。
Abstract We obtain sharp $L^{p}$ bounds for oscillatory integral operators with generic homogeneous polynomial phases in several variables. The phases considered in this paper satisfy the rank one condition that is an important notion introduced by Greenleaf, Pramanik, and Tang. Under certain additional assumptions, we can establish sharp damping estimates with critical exponents to prove endpoint $L^{p}$ estimates.