RESEARCH ARTICLE

A restriction theorem for oscillatory integral operator with certain polynomial phase

  • Shaozhen XU ,
  • Dunyan YAN
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  • School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received date: 17 Sep 2016

Accepted date: 27 Sep 2016

Published date: 06 Jul 2017

Copyright

2017 Higher Education Press and Springer-Verlag Berlin Heidelberg

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 Sn1 for this operator is obtained. Moreover, we obtain a necessary condition which ensures validity of the restriction theorem.

Cite this article

Shaozhen XU , Dunyan YAN . A restriction theorem for oscillatory integral operator with certain polynomial phase[J]. Frontiers of Mathematics in China, 2017 , 12(4) : 967 -980 . DOI: 10.1007/s11464-017-0637-0

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