Oscillatory integrals on unit square along surfaces |
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| Authors: | Jiecheng Chen Dashan Fan Huoxiong Wu Xiangrong Zhu |
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| Institution: | 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 Q
2 = 0, 1]2 be the unit square in two-dimensional Euclidean space ℝ2. We study the L
p
boundedness of the oscillatory integral operator T
α,β
defined on the set ℒ(ℝ2+n
) of Schwartz test functions by
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$
T_{\alpha ,\beta } f(u,v,x) = \int_{Q^2 } {\frac{{f(u - t,v - s,x - \gamma (t,s))}}
{{t^{1 + \alpha _1 } s^{1 + \alpha _2 } }}} e^{it - \beta _{1_s } - \beta _2 } dtds,
$
T_{\alpha ,\beta } f(u,v,x) = \int_{Q^2 } {\frac{{f(u - t,v - s,x - \gamma (t,s))}}
{{t^{1 + \alpha _1 } s^{1 + \alpha _2 } }}} e^{it - \beta _{1_s } - \beta _2 } dtds,
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| Keywords: | Oscillatory integral singular integral unit square surface product space |
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