Geodesic
Sharp Bounds for Oscillatory Integral Operators with Homogeneous Polynomial Phases
Canadian mathematical bulletin, Tome 63 (2020) no. 4, pp. 771-786

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DOI

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.
DOI : 10.4153/S000843951900081X
Mots-clés : oscillatory integral operator, homogeneous polynomial phase, rank one condition, optimal decay 
He, Danqing; Shi, Zuoshunhua. Sharp Bounds for Oscillatory Integral Operators with Homogeneous Polynomial Phases. Canadian mathematical bulletin, Tome 63 (2020) no. 4, pp. 771-786. doi: 10.4153/S000843951900081X
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     title = {Sharp {Bounds} for {Oscillatory} {Integral} {Operators} with {Homogeneous} {Polynomial} {Phases}},
     journal = {Canadian mathematical bulletin},
     pages = {771--786},
     year = {2020},
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     doi = {10.4153/S000843951900081X},
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