| 程美芳,刘慧慧,肖诚诚.某类振荡积分算子在Lebesgue空间及Wiener共合空间上的映射性质*[J].数学年刊A辑,2022,43(3):301~312 |
| 某类振荡积分算子在Lebesgue空间及Wiener共合空间上的映射性质* |
| Mapping Properties of Certain Oscillatory Integral on Lebesgue and Wiener Amalgam Spaces |
| Received:October 29, 2020 Revised:November 16, 2021 |
| DOI：10.16205/j.cnki.cama.2022.0020 |
| 中文关键词: Wiener共合空间, Lebesgue空间, 振荡积分算子, 调幅函数空间 |
| 英文关键词:Wiener amalgam spaces, Lebesgue spaces, Oscillatory integral operator, Modulation spaces |
| 基金项目:国家自然科学基金 (No.11201003, No.11771223) 和安徽省高校自然科学基金(No.KJ2017ZD27) |
| Author Name | Affiliation | | CHENG Meifang | Corresponding author. School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, Anhui, China. | | LIU Huihui | College of Mathematics and Statistics, Fuyang Normal University, Fuyang 236037, Anhui, China. | | XIAO Chengcheng | School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002,Anhui, China. |
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| 中文摘要: |
| 假设 β1 > 3α1 > 0, β2 > 3α2 > 0,给定函数f(x) ∈ S(R3), 定义算子Tα,β如下:Tα,βf(x,y,z) = p.v.ZTQ2f(x- t, y-s, z-γ(t)h(s)) e-2πit-β1 s-β2/t1+α1 s1+α2dtds.本文主要考虑如上定义的算子Tα,β在Lebesgue空间Lp(R3)及Wiener共合空间W(FLp, Lq)(R3)上的有界性. 这里 Q2 = [0, 1] × [0, 1], γ(t), h(s)满足适当的条件.作为应用, 本文还考虑了带粗糙核的奇异积分算子在乘积空间上的有界性. |
| 英文摘要: |
| Suppose β1 > 3α1 > 0, β2 > 3α2 > 0. In this paper, the authors mainly consider the mapping properties of the oscillatory integral operator Tα,β defined on the Schwartz function spaces S(R3) by Tα,βf(x,y,z) = p.v.ZTQ2p.v.ZTQ2f(x- t, y-s, z-γ(t)h(s)) e-2πit-β1 s-β2/t1+α1 s1+α2dtds. on Lebesgue spaces Lp(R3) and Wiener amalgam spacesW(FLp, Lq)(R3), where Q2 = [0, 1] × [0, 1] and γ(t), h(s) satisfy some appropriate conditions. As applications, they also investigate the boundedness of a rough singular integral operator on the product spaces. |
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