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Almost Everywhere Convergence of the Cesàro Means of Two Variablewalsh–Fourier Series with Variable Parameters

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Ukrainian Mathematical Journal Aims and scope

It is shown that the maximal operator of some (C, βn)-means of cubical partial sums of two variable Walsh–Fourier series of integrable functions is of weak type (L1,L1). Moreover, the (C, βn)-means \( {\sigma}_{2^n}^{\beta_n}f \) of the function f ∈ L1 converge a.e. to f for f ∈ L1(I2), where I is the Walsh group for some sequences 1 > βn ↘ 0.

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Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, Debrecen, Hungary

    A. A. Abu Joudeh & G. Gát

Authors
  1. A. A. Abu Joudeh
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  2. G. Gát
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Correspondence to A. A. Abu Joudeh.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 3, pp. 291–307, March, 2021. Ukrainian DOI: 10.37863/umzh.v73i3.196.

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Joudeh, A.A.A., Gát, G. Almost Everywhere Convergence of the Cesàro Means of Two Variablewalsh–Fourier Series with Variable Parameters. Ukr Math J 73, 337–358 (2021). https://doi.org/10.1007/s11253-021-01928-9

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  • DOI: https://doi.org/10.1007/s11253-021-01928-9

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