Sharp Lp decay of oscillatory integral operators with certain homogeneous polynomial phases in several variables
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摘要:
In this paper,we obtain the Lp decay of oscillatory integral operators Tλ with certain homogeneous polynomial phase functions of degree d in (n + n)-dimensions;we require that d > 2n.If d/(d-n) < p < d/n,the decay is sharp and the decay rate is related to the Newton distance.For p =d/n or d/(d-n),we obtain the almost sharp decay,where "almost" means that the decay contains a log(λ) term.For otherwise,the Lp decay of Tλ is also obtained but not sharp.Finally,we provide a counterexample to show that d/(d-n) ≤ p ≤ d/n is not necessary to guarantee the sharp decay.