广义加权空间关于卷积的稳定性及应用  

The stability and applications of convolution on the generalized weighted spaces

作　　者：薛婷[1] 藏雅妮 陈艳妮[1] XUE Ting;ZANG Yani;CHEN Yanni(School of Mathematics and Statistics,Shaanxi Normal University,710119,Xi'an,Shaanxi,PRC)

机构地区：[1]陕西师范大学数学与统计学院,陕西省西安市710119

出　　处：《曲阜师范大学学报(自然科学版)》2025年第2期1-8,F0002,共9页Journal of Qufu Normal University(Natural Science)

基　　金：国家自然科学基金(11971283).

摘　　要：该文以算子论与经典复分析为理论基础,利用旋转不变gauge范数代替常规‖·‖_(p)范数,系统研究广义加权勒贝格空间理论.通过在加权空间上定义新的加权卷积,刻画广义加权空间的代数稳定性,进而解决逼近单位元在卷积运算下的收敛性问题.In this paper,based on the operator theory and classical complex analysis,we deeply study the generalized weighted Lebesgue spaces by replacing the classical weighted L p-norms by a more general class of rotationally symmetric gauge norms.Due to the definitions and properties of the weighted convolution,we characterize the algebraic stability of the generalized weighted spaces,and then apply the theory to solve the convergence problems related to the approximate identity elements with respect to the convolution.

关 键 词：旋转不变gauge范数 加权勒贝格空间 卷积 稳定性 逼近单位元 

分 类 号：O177.2[理学—数学]