Frontiers of Mathematics in China

 Front. Math. China    2017, Vol. 12 Issue (4) : 967-980     DOI: 10.1007/s11464-017-0637-0
 RESEARCH ARTICLE |
A restriction theorem for oscillatory integral operator with certain polynomial phase
Shaozhen XU(), Dunyan YAN
School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
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 Abstract We consider the oscillatory integral operator $Tα,mf(x)=∫?nei(x1α1y1m+?+xnαnynm)f(y)dy$, where the function f is a Schwartz function. In this paper, the restriction theorem on $Sn−1$ for this operator is obtained. Moreover, we obtain a necessary condition which ensures validity of the restriction theorem. Corresponding Authors: Shaozhen XU Issue Date: 06 July 2017
 Cite this article: Shaozhen XU,Dunyan YAN. A restriction theorem for oscillatory integral operator with certain polynomial phase[J]. Front. Math. China, 2017, 12(4): 967-980. URL: http://journal.hep.com.cn/fmc/EN/10.1007/s11464-017-0637-0 http://journal.hep.com.cn/fmc/EN/Y2017/V12/I4/967