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

作　　者：程美芳 刘慧慧 肖诚诚 CHENG Meifang;LIU Huihui;XIAO Chengcheng(Corresponding author.School of Mathematics and Statistics,Anhui Normal University,Wuhu 241002,Anhui,China;College of Mathematics and Statistics,Fuyang Normal University,Fuyang 236037,Anhui,China)

机构地区：[1]安徽师范大学数学与统计学院,安徽芜湖241002 [2]阜阳师范大学数学与统计学院,安徽阜阳236037

出　　处：《数学年刊（A辑）》2022年第3期301-312,共12页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11201003,No.11771223);安徽省高校自然科学基金(No.KJ2017ZD27)的资助。

摘　　要：假设β_(1)>3α_(1)>0,β_(2)>3α_(2)>0,给定函数f(x)∈S(R^(3)),定义算子T_(α,β)如下:T_(α,β)f(x,y,z)=p.v∫_Q^(2)f(x-t,y-s,z-γ(t)h(s))^(e^(-2πit^(-β_(1_(s))-β_(2))))/t^(1)+α_(1)s^(1)+α^(2)dtds.本文主要考虑如上定义的算子T_(α,β)在Lebesgue空间L^(p)(R^(3))及Wiener共合空间W(FL^(p),L^(q))(R^(3))上的有界性.这里Q^(2)=[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.Suppose,β_(1)>3α_(1)>0,β_(2)>3α_(2)>0.In this paper,the authors mainly consider the mapping properties of the oscillatory integral operator T_(α,β) defined on the Schwartz function spaces S(R^(3))byT_(α,β)f(x,y,z)=p.v∫_Q^(2)f(x-t,y-s,z-γ(t)h(s))^(e^(-2πit^(-β_(1_(s))-β_(2))))/t^(1)+α_(1)s^(1)+α^(2)dtds on Lebesgue spaces L^(p)(R^(3)) and Wiener amalgam spaces W(FL^(p),L^(q))(R^(3)),where Q^(2)=[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.

关 键 词：Wiener共合空间 LEBESGUE空间 振荡积分算子 调幅函数空间 

分 类 号：O174.2[理学—数学]