Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, ul. Szafrana 4a, 65-516 Zielona Góra, Poland
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 and
give a sufficient and necessary condition for weighted 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 .