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Frontiers of Mathematics in China

Front. Math. China    2017, Vol. 12 Issue (4) : 967-980     DOI: 10.1007/s11464-017-0637-0
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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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 Sn1 for this operator is obtained. Moreover, we obtain a necessary condition which ensures validity of the restriction theorem.

Keywords Restriction theorem      oscillatory integral operator      L2 boundedness      optimal estimate      necessary condition     
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.
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Shaozhen XU
Dunyan YAN
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