摘要
本文研究了广义球面平均算子S^(γ)在α-模空间的导数估计,即算子ə^(β)S^(γ)在α-模空间的有界性,该算子在调和分析以及各应用分支中都具有一定的理论价值.本文首先研究了该算子在模空间的有界性,由于模空间的分解方式具有较好的性质,本文通过精细的计算和格点估计得到了该算子在模空间全指标范围有界的充要条件.随后,本文研究了该算子在一般的α-模空间的有界性,得到了有界性成立的充分条件和必要条件.
In this paper,we study the derivative estimates of the generalized spherical average operator S^(γ)inα-modulation space,that is,the boundedness of the operatorə^(β)S^(γ)inα-modulation space.This operator has certain theoretical value in the field of harmonic analysis and some other applied disciplines.In this paper,we first study the boundedness of this operator in the modulation space.Due to some good properties of the decomposition of modulation space,the necessary and sufficient conditions for the boundedness of this operator in the full index range of modulation space are obtained by some fine calculation and lattice estimation.Then,we obtain the sufficient and necessary conditions for the boundedness of this operator in the generalα-modulation space.
作者
周燕
吴小梅
黄强
ZHOU Yan;WU Xiaomei;HUANG Qiang(Department of Mathematics,College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua,Zhejiang,321004,P.R.China;Department of Mathematics,Jiaxing University,Jiaxing,Zhejiang,314001,P.R.China)
出处
《数学进展》
CSCD
北大核心
2023年第6期1085-1102,共18页
Advances in Mathematics（China）
基金
国家自然科学基金(No.11801518)
关键词
广义球面平均算子
模空间
α-模空间
波算子
generalized spherical average operator
modulation space
α-modulation space
wave operator
