## $$L^1$$-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.)

Zbl 0696.42005
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