Embedding relations connected with strong approximation of Fourier series. (English) Zbl 1271.42005
Summary: We consider the embedding relation between the class \(W^qH_\beta^\omega\), including only odd functions, and a set of functions defined via the strong means of Fourier series of odd continuous functions. We establish an improvement of a recent theorem of R. J. Le and S. P. Zhou [Math. Inequal. Appl. 11, No. 4, 749–756 (2008; Zbl 1159.42002)] which is a generalization of S. Tikhonov’s results [Anal. Math. 31, No. 3, 183–194 (2005; Zbl 1120.42002)]. We also extend L. Leindler’s theorem [Anal. Math. 31, No. 3, 175–182 (2005; Zbl 1140.42001)] concerning sequences of Fourier coefficients.
MSC:
| 42A20 | Convergence and absolute convergence of Fourier and trigonometric series |
| 42A32 | Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) |
References:
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