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Generalization on Some Theorems of L^1-Convergence of Certain Trigonometric Series
並列摘要
In this paper we study L^1-convergence of the r-th derivatives of Fourier series with complex-valued coefficients. Namely new necessary-sufficient conditions for L^1-convergence of the r-th derivatives of Fourier series are given. These results generalize corresponding theorems proved by several authors (see [7], [10], [13], [19]). Applying the Wang-Telyakovskii class (BV)(superscript σ subscript r), σ＞0, r=0, 1, 2,… we generalize also the theorem proved by Garrett, Rees and Stanojević in [5]. Finally, for σ=1 some corollaries of this theorem are given.
延伸閱讀
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