Almost everywhere convergence of Cesàro means of two variable Walsh – Fourier series with varying parameteres

  • A. A. Abu Joudeh Inst. Math., Univ. Debrecen, Hungary
  • G. Gát Inst. Math., Univ. Debrecen, Hungary
Keywords: Cesàro means with varying parameters, two-dimensional Walsh-Fourier series, Marcinkiewicz means

Abstract

UDC 517.5

We prove that the maximal operator of some $(C , \beta_{n})$ means of cubical partial sums of two variable Walsh – Fourier series of integrable functions is of weak type $(L_1,L_1)$. Moreover, the $ (C , \beta_{n})$-means $\sigma_{2^n}^{\beta_{n}} f$ of the function $ f \in L_{1} $ converge a.e. to $f$ for $ f \in L_{1}(I^2) $, where $I$ is the Walsh group for some sequences $1> \beta_n\searrow 0$.

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Published
11.03.2021
How to Cite
Abu Joudeh , A. A., and G. Gát. “Almost Everywhere Convergence of Cesàro Means of Two Variable Walsh – Fourier Series With Varying Parameteres”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 3, Mar. 2021, pp. 291 -07, doi:10.37863/umzh.v73i3.196.
Section
Research articles