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Journal of Function Spaces
Volume 2014, Article ID 201801, 13 pages
Research Article

Estimates of Modulus of Continuity of Generalized Bounded Variation Classes

1School of Mathematical Sciences, BCMIIS, Capital Normal University, Beijing 100048, China
2NO. 2 Middle School of Changping, Beijing 102208, China

Received 28 February 2014; Accepted 11 April 2014; Published 4 May 2014

Academic Editor: Józef Banaś

Copyright © 2014 Heping Wang and Zhaoyang Wu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Some sharp estimates of the modulus of continuity of classes of -bounded variation are obtained. As direct applications, we obtain estimates of order of Fourier coefficients of functions of -bounded variation, and we also characterize some sufficient and necessary conditions for the embedding relations . Our results include the corresponding known results of the class as a special case.