沿超曲面的振荡奇异积分在加权Wiener共合空间上的有界性  

Boundedness of oscillatory singular integrals along hypersurfaces on weighted Wiener amalgam spaces

作　　者：刘慧慧 唐剑 赵金虎 LIU Huihui;TANG Jian;ZHAO Jinhu(School of Mathematics and Statistics,Fuyang Normal University,Fuyang Anhui 236037,China)

机构地区：[1]阜阳师范大学数学与统计学院,安徽阜阳236037

出　　处：《湖北大学学报（自然科学版）》2022年第6期659-667,共9页Journal of Hubei University：Natural Science

基　　金：国家自然科学基金(11801081、12102093);安徽省高校自然研究项目(KJ2020A0529、KJ2020A0540);阜阳师范大学自然科学一般项目(2021FSKJ13)资助。

摘　　要：Wiener共合空间是调和分析中一类重要的函数空间,而振荡型奇异积分算子是调和分析中常见的一类重要算子.为进一步研究此类算子在加权Wiener共合空间上的有界性,本研究借助函数分解和振荡估计证明某类沿超曲面的振荡型强奇异积分算子在加权Wiener共合空间上的有界性.此外,讨论某类沿齐次超曲面的强奇异积分算子在加权Wiener共合空间上的映射性质,在一定程度上蕴含了关于Wiener共合空间比经典的Lebesgue空间更适合研究奇异积分算子的映射性质.Wiener amalgam spaces are important function spaces in harmonic analysis, and oscillatory singular integral operators are common and important operators in harmonic analysis. In order to further study the boundedness of such operators on weighted Wiener amalgam spaces, we proved the boundedness of certain oscillatory hypersingular integral operators along hypersurfaces on weighted Wiener amalgam spaces by means of function decomposition and oscillatory integral estimation. In addition, the mapping properties of some kinds of hypersingular integral operators along homogeneous hypersurfaces on weighted Wiener amalgam spaces were discussed, which implied that Wiener amalgam spaces were more suitable for studying the mapping properties of singular integral operators than classical Lebesgue spaces.

关 键 词：Wiener共合空间 奇异积分算子 调幅空间 

分 类 号：O174.2[理学—数学]