几乎处处T的收敛意味着对可积函数的维伦金系统的收敛

Ukrains’kyi Matematychnyi Zhurnal Pub Date : 2023-07-25 DOI:10.37863/umzh.v75i7.7163

N. Nadirashvili

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引用次数: 0

摘要

对于单调系数生成的Vilenkin系统，证明并讨论了T均值极大算子的一些新的弱型(1,1)不等式。我们也应用这些结果来证明这些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

UDC 517.5 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 monotone coefficients. We also apply these 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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Ukrains’kyi Matematychnyi Zhurnal

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