Abstract
A Sjölin–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 \(L {\rm log}^{+} L {\rm log}^{+} {\rm log}^{+} {\rm log}^{+} L\).
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The author would like to thank the referee for valuable remarks.
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Oniani, G. On Sjölin–Soria–Antonov type extrapolation for locally compact groups and a.e. convergence of Vilenkin–Fourier series. Acta Math. Hungar. 163, 429–436 (2021). https://doi.org/10.1007/s10474-020-01090-x
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DOI: https://doi.org/10.1007/s10474-020-01090-x