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Almost everywhere convergence of \((C,\alpha)\)-means of quadratical partial sums of double Vilenkin-Fourier series. (English) Zbl 1107.42006

Summary: We prove that the maximal operator of the \((C,\alpha)\)-means of quadratical partial sums of double Vilenkin-Fourier series is of weak type \((1,1)\). Moreover, the \((C,\alpha)\)-means \(t_{n}^{\alpha}f\) of a function \(f\in L^{1}\) converge a.e. to \(f\) as \(n\rightarrow \infty\).

MSC:

42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
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