ON THE MAXIMAL ERGODIC THEOREM.
ON THE MAXIMAL ERGODIC THEOREM.
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DOI：
10.1073/pnas.47.12.1894
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发表时间：
1961-12
影响因子：
11.1
通讯作者：
Elias M. Stein
中科院分区：
文献类型：
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作者：
Elias M. Stein
对于p = 1的替代结果。这个定理包含了对单参数半群T '，t30，满足上述条件（1）和（2）的类似定理.这些极大值定理对于算子平均值的几乎处处存在性和相应极限的范数意义是众所周知的。在某些问题中，例如在热方程、调和函数和其他微分方程的半群中，正确的分析问题是处理非平均极限lim Tt（f）的问题。我们要处理的问题是，
with a substitute result for p = 1. This theorem implies the analogue for one-parameter semi-groups T', t 3 0, satisfying conditions like (1) and (2) above. These maximal theorems have wellknown implications for the existence almost everywhere and in the norm of the corresponding limits of operator averages. In some problems, such as in semi-groups for the heat equation, harmonic functions, and other differential equations, the right analytic problem is the one dealing with the unaveraged limit, lim Tt(f). The question we shall deal with is when this