求微分基的中值方法
A median approach to differentiation bases
摘要：
我们研究了一个版本的Lebesgue微分定理，其中积分平均值被取代的Busemann-Feller微分基地的中位数。我们的主要结果给出了相应的中值极大函数的微分性质的几个特征。作为应用，我们研究点态行为Besov和Triebel-Lizorkin空间，功能不一定是局部可积的。我们的大多数结果也适用于度量测度空间上定义的函数。
英文摘要：
We study a version of the Lebesgue differentiation theorem in which the integral averages are replaced with medians over Busemann--Feller differentiation bases. Our main result gives several characterizations for the differentiation property in terms of the corresponding median maximal function. As an application, we study pointwise behaviour in Besov and Triebel--Lizorkin spaces, where functions are not necessarily locally integrable. Most of our results apply also for functions defined on metric measure spaces.
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