JIPAM

A Note on the Magnitude of Walsh Fourier Coefficients  
 
  Authors: B. L. Ghodadra, J. R. Patadia,  
  Keywords: Functions of $p-$bounded variation, $phi-$bounded variation, $p-Lambda-$bounded variation and of $phi-Lambda-$bounded variation, Walsh Fourier coefficients, Integral modulus continuity of order $p$.  
  Date Received: 11/03/08  
  Date Accepted: 07/05/08  
  Subject Codes:

42C10, 26D15.

  
  Editors: Laszlo Leindler,  
 
  Abstract:

In this note, the order of magnitude of Walsh Fourier coefficients for functions of the classes $ BV^{(p)} (pge 1)$, $ phi BV$, $ Lambda BV^{(p)}$ $ (pge 1)$ and $ phi Lambda BV$ is studied. For the classes $ BV^{(p)}$ and $ phi BV,$ Taibleson-like technique for Walsh Fourier coefficients is developed.

However, for the classes $ Lambda BV^{(p)}$ and $ phi Lambda BV$ this technique seems to be not working and hence classical technique is applied. In the case of $ Lambda BV,$ it is also shown that the result is best possible in a certain sense. ;


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