Estimates for an oscillatory integral operator related to restriction to space curves期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Estimates for an oscillatory integral operator related to restriction to space curves

Authors:	Jong-Guk Bak Sanghyuk Lee

Affiliation:	Pohang University of Science and Technology and The Korea Institute for Advanced Study ; Pohang University of Science and Technology, Pohang 790-784, Korea

Abstract:	We consider the oscillatory integral operator defined by $begin{displaymath}T_lambda f(x)=int_{mathbb R} e^{ilambdaphi(x,t)}a(x,t) f(t)dtend{displaymath}$ where , $ain C_c^infty(mathbb{R} ^ntimes mathbb{R} )$ and is a real-valued function in $C^infty(mathbb{R} ^ntimes mathbb{R} )$ . This operator may be thought of as a variable-curve version of the adjoint of the Fourier restriction operator for space curves. Under a certain nondegeneracy condition on , we obtain estimates for $T_{lambda}$ with a suitable bound for the operator norm $Vert T_lambda Vert _{L^pto L^q}$ . This generalizes a result of Hörmander for the plane to higher dimensions.

Keywords:	Oscillatory integral restriction theorem

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