Generalization on some theorems of $ L^1 $-convergence of certain trigonometric series
Keyword(s):
Sigma 1
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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 $ ({\bf B}{\bf V})_r^\sigma $, $ \>\sigma>0 $, $ \>r=0,1,2,\ldots\, $ we generalize also the theorem proved by Garrett, Rees and Stanojevi\'{c} in [5]. Finally, for $ \sigma=1 $ some corollaries of this theorem are given.
Keyword(s):
2007 ◽
Vol 44
(1)
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pp. 35-47
2019 ◽
Vol 33
(29)
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pp. 1950351
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2018 ◽
Vol 52
(2)
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pp. 02LT04
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1980 ◽
Vol s3-41
(2)
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pp. 217-253
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