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Sharp Bounds for Oscillatory Integral Operators with Homogeneous Polynomial Phases

Part of: Integral, integro-differential, and pseudodifferential operators Harmonic analysis in several variables

Published online by Cambridge University Press:  20 December 2019

Danqing He  and
Zuoshunhua Shi
Danqing He
Affiliation:
School of Mathematical Sciences, Fudan University, 220 Handan Road, Shanghai200433, People’s Republic of China Email: hedanqing@fudan.edu.cn
Zuoshunhua Shi
Affiliation:
School of Mathematics and Statistics, Central South University, Changsha, People’s Republic of China Email: shizsh@csu.edu.cn
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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.

Keywords

oscillatory integral operatorhomogeneous polynomial phaserank one conditionoptimal decay

MSC classification

Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 47G10: Integral operators
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 4 , December 2020 , pp. 771 - 786
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Copyright
© Canadian Mathematical Society 2019

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Footnotes

Danqing He was supported by NNSF of China (No. 11701583). Zuoshunhua Shi was supported in part by NNSF of China under Grant No. 11701573.

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