可变Caldero′n-Zygmund核的分数次积分算子在HK_q^(α,p)上的连续性

The Continuity of Fractional Integrals with VariableCaldero′n-Zygmund Kernels on HK_q^(α,p)

可变Caldero′n-Zygmund核分数次积分算子是一种特殊的分数次积分算子,而分数次积分算子是调和分析的重要算子,它不仅在调和分析中有着重要的地位而且在偏微分方程中也具有及其重要的作用,所以有必要研究可变Caldero′n-Zygmund核分数次积分算子的一些性质.文章改进了文[5]的结论,运用经典调和分析的理论和方法进一步讨论了可变Caldero′n-Zygmund核分数次积分算子TΩ,μ在Herz型Hardy空间上的连续性,得到如下结论:当Ω(x,z)∈L∞(Rn)×Ls(Sn-1)(s≥1)且满足Ls-Dini条件时,可变Caldero′n-Zygmund核分数次积分算子TΩ,μ是从Herz型Hardy空间到Herz型Hardy空间或Herz型空间连续的.

Fractional integral operators with variable Calderon-Zygmund kernels are special cases of the fractional integral operators. It is well known that the singular integral operators, fractional integral operators and their commutators play profound and extentive roles in both harmonic analysis and partial differential equations. Hence to study the problem on the continuity of fractional integral operators with variable Calderon-Zygmund kernels is interested by many authors. The paper improves a result obtained by Zhang （see[5]） regarding the fractional integral and investigates the continuity of the fractional integral operators with variable Calderon-Zygmund kernels on the Herz type Hardy spaces and Herz-type spaces, or to be exact, the fractional integral operator TΩ,μ is bounded from HKq1^a,p1 （R^n） to HKq2^a,p2 （R^n） or HKq2^a,p2 （R^n） under certain assumptions on the kernel.