Divergence almost everywhere of square partial sums of Fourier-Walsh series of integrable functions (Q1905244)
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scientific article; zbMATH DE number 830689
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Divergence almost everywhere of square partial sums of Fourier-Walsh series of integrable functions |
scientific article; zbMATH DE number 830689 |
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Divergence almost everywhere of square partial sums of Fourier-Walsh series of integrable functions (English)
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28 October 1996
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The author shows that for double Walsh-Fourier series, finiteness of the Lebesgue constants is \textit{not} sufficient for a.e. convergence. Indeed, he shows that there exist a sequence \(\{n_k\}\) of natural numbers and an integrable function \(f(x, y)\) such that \(\sup L_{n_k}= \infty\) but the square partial sums \(S_{n_k, n_k} f\) diverge a.e. on the unit square.
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double Walsh-Fourier series
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Lebesgue constants
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square partial sums
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