We prove that there exists a continuous function on \([0,1]^2\), with a certain smoothness, whose double Fourier–Walsh series diverges on a set of positive measure by rectangles. Similar theorem is proved also for the double Walsh–Kaczmarz system.

中文翻译：

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关于连续函数的双重傅里叶-沃尔什和傅里叶-沃尔什-Kaczmarz级数的散度

我们证明在\（[0,1] ^ 2 \）上存在一个具有一定平滑度的连续函数，其双傅里叶-沃尔什级数在一组由矩形组成的正度量上发散。双沃尔什-卡茨马尔兹系统也证明了类似的定理。