Sharp L^p decay of oscillatory integral operators with certain homogeneous polynomial phases in several variables  

作　　者：Shaozhen Xu Dunyan Yan 

机构地区：[1]School of Mathematical Sciences, University of Chinese Academy of Sciences

出　　处：《Science China Mathematics》2019年第4期649-662,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11471309, 11271162 and 11561062)

摘　　要：In this paper, we obtain the L^p decay of oscillatory integral operators T_λ with certain homogeneous polynomial phase functions of degree d in(n + n)-dimensions; we require that d > 2 n. 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 L^p decay of T_λ 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.In this paper, we obtain the L^p decay of oscillatory integral operators T_λ with certain homogeneous polynomial phase functions of degree d in(n + n)-dimensions; we require that d > 2 n. 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 L^p decay of T_λ 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.

关 键 词：OSCILLATORY integral operators SHARP L^p DECAY several variables NEWTON distance 

分 类 号：O1[理学—数学]