\(L^1\)-convergence of double Vilenkin series. (English) Zbl 1528.42036
Summary: We give necessary and sufficient conditions for \(L^1\) convergence of double Vilenkin series whose coefficients form a double null sequence of bounded variation. Also we study the existence of the special form of Riemann improper integral for sum of this series.
MSC:
| 42C10 | Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) |
| 42A20 | Convergence and absolute convergence of Fourier and trigonometric series |
References:
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