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Almost Everywhere Convergence of Cesàro-Marczinkiewicz Means of Two-Dimensional Fourier Series on the Group of \(2\)-Adic Integers

Abstract

In this paper, we prove the almost everywhere convergence of the \((C,\alpha)\) Marczinkiewicz-means of integrable functions on the group of the two-dimensional \(2\)-adic integers.

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Funding

The first author is supported by the Hungarian National Foundation for Scientific Research (OTKA), grant no. K111651 and by project EFOP-3.6.2-16-2017-00015 supported by the Europea Union, cofinanced by the European Social Fund.

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Correspondence to György Gát or Gábor Lucskai.

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Gát, G., Lucskai, G. Almost Everywhere Convergence of Cesàro-Marczinkiewicz Means of Two-Dimensional Fourier Series on the Group of \(2\)-Adic Integers. P-Adic Num Ultrametr Anal Appl 14, 116–137 (2022). https://doi.org/10.1134/S2070046622020030

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  • DOI: https://doi.org/10.1134/S2070046622020030

Keywords

  • group of \(2\)-adic integers
  • character system
  • convergence of two-dimensional Cesàro-Marczinkiewicz means
  • maximal operators