Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 485705, 19 pages
Research Article

On Weighted Lp Integrability of Functions Defined by Trigonometric Series

Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, ul. Szafrana 4a, 65-516 Zielona Góra, Poland

Received 26 January 2010; Accepted 13 April 2010

Academic Editor: László Losonczi

Copyright © 2010 Bogdan Szal. 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.


We introduce a new class of sequences called GM¯θr and give a sufficient and necessary condition for weighted Lp integrability of trigonometric series with coefficients to belong to the above class. This is a generalization of the result proved by M. Dyachenko and S. Tikhonov (2009). Then we discuss the relations among the weighted best approximation and the coefficients of trigonometric series. Moreover, we extend the results of B. Wei and D. Yu (2009) to the class GM¯θr.