变指标齐次Triebel-Lizorkin空间和Besov空间的刻画  

Characterizations of Triebel-Lizorkin spaces and Besov spaces with variable exponents

作　　者：白腾飞 徐景实 BAI Tengfei;XU Jingshi(School of Mathenatics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2024年第1期19-22,共4页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(12161022);广西自然科学基金(2020GXNSFAA159085)。

摘　　要：为研究变指标齐次Triebel-Lizorkin空间与Besov空间的Riesz位势刻画和导数刻画,通过傅里叶变换和归纳法,当变指标函数满足对数Hölder连续时,得到Riesz位势算子在变积分指标、变光滑指标与变求和指标的齐次Triebel-Lizorkin空间和变积分指标、变光滑指标与变求和指标的齐次Besov空间上的有界性。进而当变指标函数满足对数Hölder连续时,得到了变积分指标、变光滑指标和变求和指标的齐次Triebel-Lizorkin空间与变积分指标、变光滑指标和变求和指标的齐次Besov空间的Riesz位势刻画和导数刻画。The purpose of this paper is to research the characterizations of homogeneous Triebel-Lizorkin spaces and Besov spaces with variable integral exponent in terms of Riesz potential and derivative.By the Fourier transformation and induction method,we show that the Riesz potential operator is bounded on homogeneous Triebel-Lizorkin spaces and Besov spaces with variable integral exponent,variable smooth exponent,and variable summation exponent,while these exponents are log-Hölder continuous.Then characterizations of these spaces in terms of Riesz potential and derivative are obtained when exponents are log-Hölder continuous.

关 键 词：RIESZ位势 TRIEBEL-LIZORKIN空间 BESOV空间 变指标 

分 类 号：O177[理学—数学]