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

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.