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Some Results on $L^1$ Approximation of the $r$-th Derivate of Fourier Series  
 
  Authors: Zivorad Tomovski,  
  Keywords: $L^1$-approximation, Fourier series, Sidon-Telyakovskii class, Telyakovskii inequality.  
  Date Received: 22/09/99  
  Date Accepted: 18/10/01  
  Subject Codes:

26D15,42A20

  
  Editors: Alexander G. Babenko,  
 
  Abstract:

In this paper we obtain the conditions for $ L^{1}$-convergence of the $ r$-th derivatives of the cosine and sine trigonometric series. These results are extensions of corresponding Sidon's and Telyakovskii's theorems for trigonometric series (case: $ r=0$).
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