Certain oscillatory integrals on unit square and their applications  

作　　者：FAN DaShan WU HuoXiong 

机构地区：[1]Department of Mathematics,University of Wisconsin-Milwaukee,Milwaukee,WI 53217,USA [2]School of Mathematical Sciences,Xiamen University,Xiamen 361005,China

出　　处：《Science China Mathematics》2008年第10期1895-1903,共9页中国科学：数学（英文版）

基　　金：the National Natural Science Foundation of China (Grant Nos. 10571122, 10371046);the Natural Science Foundation of Fujian Province of China (Grant No. Z0511004)

摘　　要：Let Q 2 = [0, 1]2 be the unit square in two dimension Euclidean space ?2. We study the L p boundedness properties of the oscillatory integral operators T α,β defined on the set S(?3) of Schwartz test functions f by $$ \mathcal{T}_{\alpha ,\beta } f(x,y,z) = \int_{Q^2 } {f(x - t,y - s,z - t^k s^j )e^{ - it^{ - \beta _1 } s^{ - \beta 2} } t^{ - 1 - \alpha _1 } s^{ - 1 - \alpha _2 } dtds} , $$ where β1 > α1 ? 0, β2 > α2 ? 0 and (k, j) ∈ ?2. As applications, we obtain some L p boundedness results of rough singular integral operators on the product spaces.Let Q2 = [0, 1]2 be the unit square in two dimension Euclidean space R2. We study the Lp boundedness properties of the oscillatory integral operators Tα,β defined on the set S(R3) of Schwartz test functions f by Tα,βf(x,y,z) = Q2 f(x - t,y - s,z - tksj)e-it-β1s-β2t-1-α1s-1-α2dtds, where β1 > α1 0, β2 > α2 0 and (k, j) ∈ R2. As applications, we obtain some Lp boundedness results of rough singular integral operators on the product spaces.

关 键 词：oscillatory integral singular integral rough kernel unit square product space 42B10 42B15 42B20 

分 类 号：O177[理学—数学]