Abstract
In this work we study the maximal operator for a class of subsequences of Nörlund logarithmic means ofWalsh–Fourier series. For such a class we prove the almost everywhere convergence of \(\left( {t_{m_n } f} \right)_n\) for every integrable function f. Besides, we establish a divergence theorem for other classes of subsequences.
абстрактный
В этой работе мы изучаем максимальный оператор для некоторого класса подпоследовательпостей логарифимических средних Нерлунда ряда Уолша-Фурье. Для такого класса мы доказываем сходимость почти всюду \(\left( {t_{m_n } f} \right)_n\) для любои ин- тегрируемои функции f. Кроме того, мы устанавливаем теорему о расходимости для других классов подпоследовательностей
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Memić, N. Almost everywhere convergence of some subsequences of the Nörlund logarithmic means of Walsh–Fourier series. Anal Math 41, 45–54 (2015). https://doi.org/10.1007/s10476-015-0104-7
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DOI: https://doi.org/10.1007/s10476-015-0104-7