Certain oscillatory integrals on unit square and their applications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

Certain oscillatory integrals on unit square and their applications

Authors:

Affiliation:

(1) Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI 53217, USA;(2) School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

Abstract:

Let Q ² = [0, 1]² be the unit square in two dimension Euclidean space ℝ². We study the L ^p boundedness properties of the oscillatory integral operators T _α,β defined on the set S(ℝ³) 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) ∈ ℝ². As applications, we obtain some L ^p boundedness results of rough singular integral operators on the product spaces. This work was supported by the National Natural Science Foundation of China (Grant Nos. 10571122, 10371046) and the Natural Science Foundation of Fujian Province of China (Grant No. Z0511004)

Keywords:

oscillatory integral singular integral rough kernel unit square product space

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