各向异性分数次积分算子的加权估计（英文）A Weighted Estimates of Anisotropic Fractional Integral Operators
张惠;齐春燕;李宝德;
摘要(Abstract)：
设A是一个扩张矩阵,α∈[0,1),p∈(1,1/α)且q:=(1/p-α)-1,如果非负函数v满足各向异性的Muckenhoupt Ap,q(A)权条件,那么各向异性的分数次极大函数f*α从Lp(Rn,vp)到Lq(Rn,vq)是有界的.作为应用,作者进一步证明了v∈Ap,q(A)当且仅当各向异性分数次积分算子Tα,A从Lp(Rn,vp)到Lq(Rn,vq)是有界的,这些结论是Muckenhoupt和Wheeden的结果在各向异性情形下的推广(Trans Amer Math Soc,192:261-274,1974).
关键词(KeyWords)： 各向异性;扩张矩阵;Muckenhoupt权;分数次积分算子;分数次极大函数
基金项目(Foundation): supported by the Natural Science Foundation of Xinjiang Uyghur Autonomous Region(2015211C283)
作者(Authors): 张惠;齐春燕;李宝德;
DOI: 10.13568/j.cnki.651094.2017.01.007
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