A class of increasing sequences of natural numbers $(n_k)$ is found for which there exists a function $f\in L[0,1)$ such that the subsequence of partial Walsh-Fourier sums $(S_{n_k}(f))$ diverge everywhere. A condition for the growth order of a function $\varphi:[0,\infty)\rightarrow[0,\infty)$ is given fulfilment of which implies an existence of above type function $f$ in the class $\varphi(L)[0,1)$.

中文翻译：

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关于部分 Walsh-Fourier 和的子序列的散度

找到一类自然数递增序列$(n_k)$，在L[0,1)$中存在一个函数$f\使得偏Walsh-Fourier和$(S_{n_k}(f )) $ 处处发散。函数 $\varphi:[0,\infty)\rightarrow[0,\infty)$ 的增长顺序的条件得到满足，这意味着在类 $\varphi( L) [0.1) $.