Oscillatory integrals on unit square along surfaces

doi:10.1007/s11464-010-0088-3

Front Math Chin

2011, Vol. 6

Issue (1) : 49-59 https://doi.org/10.1007/s11464-010-0088-3

RESEARCH ARTICLE

Oscillatory integrals on unit square along surfaces

Jiecheng CHEN^1,2, Dashan FAN³, Huoxiong WU⁴(

), Xiangrong ZHU^1,2

1. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China; 2. Department of Mathematics, Zhejiang University, Hangzhou 310027, China; 3. Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA; 4. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

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Abstract

Let Q² = [0, 1]² be the unit square in two-dimensional Euclidean space ?2. We study the L^p boundedness of the oscillatory integral operator T_α_,_β defined on the set ?(?2+n) of Schwartz test functions byTα,βf(u,v,x)=∫Q2f(u-t,v-s,x-γ(t,s))t1+α1s1+α2eit-β1s-β2dtds,where x∈?n, (u,v)∈?2, (t,s,γ(t,s))=(t,s,tp1sq1,tp2sq2,?,tpnsqn) is a surface on ?n+2, and β₁>α₁, β₂>α₂. Our results extend some known results on ?3.

Keywords Oscillatory integral singular integral unit square surface product space

Corresponding Author(s): WU Huoxiong,Email:huoxwu@xmu.edu.cn

Issue Date: 01 February 2011

Cite this article:

Jiecheng CHEN,Dashan FAN,Huoxiong WU, et al. Oscillatory integrals on unit square along surfaces[J]. Front Math Chin, 2011, 6(1): 49-59.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-010-0088-3
https://academic.hep.com.cn/fmc/EN/Y2011/V6/I1/49

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