非倍测度条件下Marcinkiewicz积分在Herz空间中的有界性Boundness of Marcinkiewicz Integral with Non Doubling Measures on Herz Spaces
张婧;
摘要(Abstract)：
考虑如下的Marcinkiewicz积分算子:M(f)(x)=[integral form n=0 to ∞│∫_(x-y)≤tk(x,y)f(y)dμ(y)│~2dt/t~3]1/2,x∈R~d,其中,μ为非倍测度.证明了它是在Herz空间Kαq,p(μ)上有界,同时也是从Herz空间Kαq,p(μ)到弱Herz空间WKqα,p(μ)上有界.
关键词(KeyWords)： Herz空间;Marcinkiewicz积分算子;弱Herz空间;非双倍测度
基金项目(Foundation): 国家自然科学基金:10261007
作者(Author): 张婧;
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参考文献(References)：
- [1]Lu Shan-zhen.Herz Type Spaces[J].Advances In Mathematics,2004,33(3):257-272.
- [2]Guoen Hu,Haibo Lin,Dachun Yang.Marcinkiewicz Integrals with Non Doubling Measures[J].Integral Equation and Operator Theory,2007,58(2):205-238.
- [3]Guo Yan,Meng Yan.Boundedness of Some Operators and Commutators In Herz Spaces With Non Doubling Measures[J].Journal of Beijing Normal University(Natural Scince),2004,40(6):725-731.
- [4]Tolsa X.BMO,H1and Cald′eron-Zygmund operators for non doubling measures[J].Math Ann,2001,319:89-149.
- [5]Chen Dong-xiang,Chen Jie-cheng.Boundedness of Marcinkiewicz Integrals With Rough kernel on Herz Spaces[J].Advances In Mathematics,2005,34(5):591-599.