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Abstract <p> We give sufficient conditions for a.e. convergence of Vilenkin-Fourier series on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\([0,1)\)</EquationSource> </InlineEquation>, pointwise one on <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\((0,1)\)</EquationSource> </InlineEquation> and uniform convergence on <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\([\varepsilon,1)\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\varepsilon\in (0,1)\)</EquationSource> </InlineEquation>, in terms of behavior of some linear means of cited above series. Also, a condition for such means to converge a.e. on <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\([0,1)\)</EquationSource> </InlineEquation> is proved. </p>

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Tauberian Tests of Convergence on Some Subsets of \([0,1)\) of Vilenkin-Fourier Series

  • 期刊论文

  • 发表日期：

    2026年5月6日

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  • N. Yu. Agafonova,
  • S. S. Volosivets

摘要

Abstract

We give sufficient conditions for a.e. convergence of Vilenkin-Fourier series on \([0,1)\) , pointwise one on \((0,1)\) and uniform convergence on \([\varepsilon,1)\) , \(\varepsilon\in (0,1)\) , in terms of behavior of some linear means of cited above series. Also, a condition for such means to converge a.e. on \([0,1)\) is proved.