一类非二重性拟度量测度空间中修正极大函数的相关估计
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摘要
研究拟度量测度空间(X,d,μ)中修正的极大函数,其中X表示集合,d表示不满足对称性的拟度量,μ表示Borel测度.通过改进已有的弱(1,1)估计,结合逼近和延拓的方法证明了修正的极大函数的(Φ,Ψ)型估计,这里Φ,Ψ是满足一定条件的连续函数,并且讨论了修正的极大函数的L1可积性.文中结果适用于Kolmogorov算子对应的Lie群.
The modified maximal functions in the quasi-metric measure space(X,d,μ)is studied,where Xis a set,dis a quasi-metric which is not symmetric,μis a Borel measure.Improving weak(1,1)type estimate,and combining with approximation and continuation method.(Φ,Ψ)type estimates by approximation and extension is established,whereΦ,Ψare continuous functions,the L1 integrability for modified maximal functions are also considered.The results can be applied to Lie groups corresponding to Kolmogorov type operators.
The modified maximal functions in the quasi-metric measure space(X,d,μ)is studied,where Xis a set,dis a quasi-metric which is not symmetric,μis a Borel measure.Improving weak(1,1)type estimate,and combining with approximation and continuation method.(Φ,Ψ)type estimates by approximation and extension is established,whereΦ,Ψare continuous functions,the L1 integrability for modified maximal functions are also considered.The results can be applied to Lie groups corresponding to Kolmogorov type operators.
引文
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[15] YOON J.Hardy-Littlewood maximal functions on Orlicz spaces[J].Bull Korean Math Soc,1999,36(2):225-231.
[16] KITA H.On maximal functions in Orlicz spaces[J].P Am Math Soc,1996,124(10):3019-3025.
[17] STEIN E M.Note on the class LlogL[J].Studia Math,1969,32:305-310.
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