非二重性拟度量测度空间中修正的极大函数定理及其应用

Modified Maximal Function Theorems in a Nondoubling Quasi-Metric Measure Space and Applications

主要研究了拟度量测度空间（X，d，μ）中修正的极大函数，其中X表示集合，μ表示不满足二重性的Borel测度，d表示不满足对称性的拟度量．本文对修正的极大函数建立了弱（1，1）估计和（Ф,Ф）型估计，其中Ф比N函数更一般．作为应用，证明了拟度量测度空间中推广的Lebesgue微分定理．本文的结果也适用于与常系数Kolmogorov型算子对应的Lie群G=（R^N＋1，o）.

We study modified maximal functions in a quasi-metric measure space （X, d, μ）, where X is a set, μ stands for the Borel measure which is not doubling, d is a quasi-metric being quasi-symmetric. We establish the weak （1, 1） estimates and （Ф, Ф） type estimates for modified maximal functions, where Ф is more general than N-functions. As applications, we prove a generalized Lebesgue differential theorem in the quasi-metric measure space; the results of this paper can be applied to the Lie group G=（R^N＋1,o） associated with the Kolmogorov type operator with constant coefficients.