对于可积函数的维伦金系统，T几乎处处收敛

Pub Date : 2023-11-25 DOI:10.1007/s11253-023-02247-x

N. Nadirashvili

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引用次数: 0

摘要

我们证明并讨论了关于单调系数生成的Vilenkin系统的T均值极大算子的一些新的弱型(1,1)不等式。我们还应用累积的结果证明了这些T均值几乎处处收敛。作为应用，我们给出了一些已知的和新的结果。

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Almost Everywhere Convergence of T Means with Respect to the Vilenkin System of Integrable Functions

We prove and discuss some new weak-type (1,1) inequalities for the maximal operators of T means with respect to the Vilenkin system generated by monotonic coefficients. We also apply the accumulated results to prove that these T means are almost everywhere convergent. As applications, we present both some well-known and new results.

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