一类振荡积分算子在Wiener共合空间上的有界性  

Boundedness Properties of Certain Oscillatory Integrals on Wiener Amalgam Space

作　　者：程美芳 孙伟 束立生 CHENG Meifang;SUN Wei;SHU Lisheng(Corresponding author. School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, Anhui, China. 2School of Mathematics and Statistics, Anhui Normal University, Wuhu 241002, 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

出　　处：《数学年刊（A辑）》2018年第2期113-126,共14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;No.KJ2015A117)的资助

摘　　要：假设a,b>0并且K_(a,b)(x)=(e^(i|x|^(-b)))/(|x|^(n+a))定义强奇异卷积算子T如下:Tf(x)=(K_(a,b)*f)(x),本文主要考虑了如上定义的算子T在Wiener共合空间W(FL^p,L^q)(R^n)上的有界性.另一方面,设α,β>0并且γ(t)=|t|~k或γ(t)=sgn(t)|t|~k.利用振荡积分估计,本文还研究了算子T_(α,β)f(x,y)=p.v∫_(-1)~1f(x-t,y-γ(t))(e^(2πi|t|^(-β)))/(t|t|~α)dt及其推广形式∧_(α,β)f(x,y,z)=∫_(Q^2)f(x-t,y-s,z-t^ks^j)e^(-2πit)^(-β_1_s-β_2)t^(-α_1-1)s^(-α_2-1)dtds在Wiener共合空间W(FL^p,L^q)上的映射性质.本文的结论足以表明,Wiener共合空间是Lebesgue空间的一个很好的替代.Suppose a, b 0 and Ka,b（x）=（ei｜x｜-b））/（｜x｜n＋a）The first task in this paper is to study the boundedness properties of the strongly singular convolution operator Tf（x） =（Ka,b＊f）（x）on Wiener amalgam spaces W（FLp,Lq）（Rn）.If α,β 0 and γ（t）=｜t｜k or γ（t） = sgn（t）｜t｜k,the second task of this paper is to investigate the mapping properties of the operator defined by Tα,βf（x,y）=p.v∫-11f（x-t,y-γ（t））（e2πi｜t｜-β）/（t｜t｜α）dt and its general form given by ∧α,βf（x,y,z）=∫Q2f（x-t,y-s,z-tksj）e-2πit-β1s-β2t-α1-1s-α2-1dtds on Wiener amalgam spaces W（FLp,Lq）. The essential tool of this paper is the oscillatory integral estimation. The results of this paper show that Wiener amalgam spaces are good substitutions for Lebesgue spaces.

关 键 词：Wiener共合空间 强奇异积分算子 调幅空间 

分 类 号：O174.2[理学—数学]