Embedding relations connected with strong approximation of Fourier series

We consider the embedding relation between the class W ^q H _β ^ω , including only odd functions and a set of functions defined via the strong means of Fourier series of odd continuous functions. We establish an improvement of a recent theorem of Le and Zhou Math. Inequal. Appl. 11(4) (2008) 749–756] which is a generalization of Tikhonov’s results Anal. Math. 31 (2005) 183–194]. We also extend the Leindler theorem Anal. Math. 31 (2005) 175–182] concerning sequences of Fourier coefficients.