We consider the embedding relation between the class WqHβω, 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.