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\(L^1\)-convergence of modified complex trigonometric sums. (English) Zbl 1016.42002

Summary: In this paper we study \(L^{1}\)–convergence of modified complex trigonometric sums introduced by B. Ram and S. Kumari [Indian J. Pure Appl. Math. 20, No. 9, 908-914 (1989; Zbl 0696.42005)] and obtain a necessary and sufficient condition for \(L^{1}\)-convergence of Fourier series under a new class \(K^\ast\) of coefficients.

MSC:

42A20 Convergence and absolute convergence of Fourier and trigonometric series
42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)

Citations:

Zbl 0696.42005
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