A Sjolin–Soria–Antonov type extrapolation theorem for locally compact $$\sigma$$ -compact non-discrete Hausdorff groups is proved. Applying this result it is shown that the Fourier series with respect to the Vilenkin orthonormal systems on the Vilenkin groups of bounded type converge almost everywhere for functions from the class $$L {\rm log}^{+} L {\rm log}^{+} {\rm log}^{+} {\rm log}^{+} L$$ .

中文翻译：

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关于局部紧群的 Sjölin-Soria-Antonov 型外推和 Vilenkin-Fourier 级数的 ae 收敛

证明了局部紧致$$\sigma$$-紧非离散Hausdorff群的Sjolin-Soria-Antonov型外推定理。应用这个结果表明，对于类 $$L {\rm log}^{+} L {\rm log} 的有界类型 Vilenkin 群上的 Vilenkin 正交系统的傅立叶级数几乎处处收敛^{+} {\rm log}^{+} {\rm log}^{+} L$$ 。